Probabilistic normed spaces /:
This book provides a comprehensive foundation in Probabilistic Normed (PN) spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A.N. Serstnev in the earl...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ :
Imperial College Press,
[2014]
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book provides a comprehensive foundation in Probabilistic Normed (PN) spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A.N. Serstnev in the early 1960s as a response to problems of best approximations in statistics. The theory was revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who provided a new, wider definition of a PN space which quickly became the standard adopted by all researchers. This book is the first wholly up-to-date and thorough investigation of the properties, uses and applications of PN spaces, based on the standard definition. Topics covered include: What are PN spaces? The topology of PN spaces. Probabilistic norms and convergence. Products and quotients of PN spaces. D-boundedness and D-compactness. Normability. Invariant and semi-invariant PN spaces. Linear operators. Stability of some functional equations in PN spaces. Menger's 2-probabilistic normed spaces. The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equations. This introduction will therefore have broad relevance across mathematical and statistical research, especially those working in probabilistic functional analysis and probabilistic geometry. |
| Beschreibung: | 1 online resource (xi, 220 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781783264698 1783264691 |
Internformat
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn890146540 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr mn||||||||| | ||
| 008 | 140908t20142014nju ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e rda |e pn |c N$T |d IDEBK |d CDX |d OTZ |d YDXCP |d OSU |d DEBSZ |d OSU |d OCLCQ |d AGLDB |d OCLCQ |d COO |d VTS |d STF |d LEAUB |d UKAHL |d OCLCO |d OCLCQ |d OCLCO |d OCLCL |d SXB |d OCLCQ |d OCLCO | ||
| 020 | |a 9781783264698 |q (electronic bk.) | ||
| 020 | |a 1783264691 |q (electronic bk.) | ||
| 020 | |z 9781783264681 |q (alk. paper) | ||
| 020 | |z 1783264683 |q (alk. paper) | ||
| 035 | |a (OCoLC)890146540 | ||
| 050 | 4 | |a QA322.2 |b .L38 2014eb | |
| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 082 | 7 | |a 515/.73 |2 23 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Lafuerza Guillén, Bernardo, |e author. | |
| 245 | 1 | 0 | |a Probabilistic normed spaces / |c Bernardo Lafuerza Guillén, Universidad de Almeria, Spain, Panackal Harikrishnan, Manipal Institute of Technology (MIT Manipal), India. |
| 264 | 1 | |a Hackensack, NJ : |b Imperial College Press, |c [2014] | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (xi, 220 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 520 | |a This book provides a comprehensive foundation in Probabilistic Normed (PN) spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A.N. Serstnev in the early 1960s as a response to problems of best approximations in statistics. The theory was revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who provided a new, wider definition of a PN space which quickly became the standard adopted by all researchers. This book is the first wholly up-to-date and thorough investigation of the properties, uses and applications of PN spaces, based on the standard definition. Topics covered include: What are PN spaces? The topology of PN spaces. Probabilistic norms and convergence. Products and quotients of PN spaces. D-boundedness and D-compactness. Normability. Invariant and semi-invariant PN spaces. Linear operators. Stability of some functional equations in PN spaces. Menger's 2-probabilistic normed spaces. The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equations. This introduction will therefore have broad relevance across mathematical and statistical research, especially those working in probabilistic functional analysis and probabilistic geometry. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a 1. Preliminaries. 1.1. Probability spaces. 1.2. Distribution functions. 1.3. The space of distance of distribution functions. 1.4. Copulas. 1.5. Triangular norms. 1.6. Triangle functions. 1.7. Multiplications. 1.8. Probabilistic metric spaces. 1.9. L[symbol] and Orlicz spaces. 1.10. Domination. 1.11. Duality -- 2. Probabilistic Normed spaces. 2.1. Probabilistic Normed spaces. 2.2. 1993: PN spaces redefined. 2.3. Special classes of PN spaces. 2.4. [symbol]-simple spaces. 2.5. EN spaces. 2.6. Probabilistic inner product spaces. 2.7. Open questions -- 3. The topology of PN spaces. 3.1. The topology of a PN space. 3.2. The uniform continuity of the probabilistic norm. 3.3. A PN space as a topological vector space. 3.4. Completion of PN spaces. 3.5. Probabilistic metrization of generalized topologies. 3.6. TIGT induced by probabilistic norms -- 4. Probabilistic norms and convergence. 4.1. The L[symbol] and Orlicz norms. 4.2. Convergence of random variables -- 5. Products and quotients of PN spaces. 5.1. Finite products. 5.2. Countable products of PN spaces. 5.3. Final considerations. 5.4. Quotients -- 6. D-boundedness and D-compactness. 6.1. The probabilistic radius. 6.2. Boundedness in PN spaces. 6.3. Total boundedness. 6.4. D-compact sets in PN spaces. 6.5. Finite dimensional PN spaces -- 7. Normability. 7.1. Normability of Serstnev spaces. 7.2. Other cases. 7.3. Normability of PN spaces. 7.4. Open questions -- 8. Invariant and semi-invariant PN spaces. 8.1. Invariance and semi-invariance. 8.2. New class of PN spaces. 8.3. Open questions -- 9. Linear operators. 9.1. Boundedness of linear operators. 9.2. Classes of linear operators. 9.3. Probabilistic norms for linear operators. 9.4. Completeness results. 9.5. Families of linear operators -- 10. Stability of some functional equations in PN spaces. 10.1. Mouchtari-Serstnev theorem. 10.2. Stability of a functional equation in PN spaces. 10.3. The additive Cauchy functional equation in RN spaces: Stability. 10.4. Stability in the quartic functional equation in RN spaces. 10.5. A functional equation in Menger PN spaces -- 11. Menger's 2-probabilistic Normed spaces. 11.1. Accretive operators in 2-PN spaces. 11.2. Convex sets in 2-PN spaces. 11.3. Compactness and boundedness in 2-PN spaces. 11.4. D-boundedness in 2-PN spaces. | |
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Normed linear spaces. |0 http://id.loc.gov/authorities/subjects/sh85092434 | |
| 650 | 6 | |a Espaces linéaires normés. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Normed linear spaces |2 fast | |
| 700 | 1 | |a Harikrishnan, Panackal, |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjG88kmjDG6c4vB9qMwgrq |0 http://id.loc.gov/authorities/names/n2014026214 | |
| 758 | |i has work: |a Probabilistic normed spaces (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGxWQKQ4ycYt83X3tDfb7d |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Lafuerza Guillén, Bernardo. |t Probabilistic normed spaces |z 9781783264681 |w (DLC) 2014018361 |w (OCoLC)879553040 |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=839691 |3 Volltext |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH27083574 | ||
| 938 | |a Coutts Information Services |b COUT |n 29748685 | ||
| 938 | |a EBSCOhost |b EBSC |n 839691 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis29748685 | ||
| 938 | |a YBP Library Services |b YANK |n 12058368 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn890146540 |
|---|---|
| _version_ | 1816882286002438144 |
| adam_text | |
| any_adam_object | |
| author | Lafuerza Guillén, Bernardo Harikrishnan, Panackal |
| author_GND | http://id.loc.gov/authorities/names/n2014026214 |
| author_facet | Lafuerza Guillén, Bernardo Harikrishnan, Panackal |
| author_role | aut aut |
| author_sort | Lafuerza Guillén, Bernardo |
| author_variant | g b l gb gbl p h ph |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA322 |
| callnumber-raw | QA322.2 .L38 2014eb |
| callnumber-search | QA322.2 .L38 2014eb |
| callnumber-sort | QA 3322.2 L38 42014EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 1. Preliminaries. 1.1. Probability spaces. 1.2. Distribution functions. 1.3. The space of distance of distribution functions. 1.4. Copulas. 1.5. Triangular norms. 1.6. Triangle functions. 1.7. Multiplications. 1.8. Probabilistic metric spaces. 1.9. L[symbol] and Orlicz spaces. 1.10. Domination. 1.11. Duality -- 2. Probabilistic Normed spaces. 2.1. Probabilistic Normed spaces. 2.2. 1993: PN spaces redefined. 2.3. Special classes of PN spaces. 2.4. [symbol]-simple spaces. 2.5. EN spaces. 2.6. Probabilistic inner product spaces. 2.7. Open questions -- 3. The topology of PN spaces. 3.1. The topology of a PN space. 3.2. The uniform continuity of the probabilistic norm. 3.3. A PN space as a topological vector space. 3.4. Completion of PN spaces. 3.5. Probabilistic metrization of generalized topologies. 3.6. TIGT induced by probabilistic norms -- 4. Probabilistic norms and convergence. 4.1. The L[symbol] and Orlicz norms. 4.2. Convergence of random variables -- 5. Products and quotients of PN spaces. 5.1. Finite products. 5.2. Countable products of PN spaces. 5.3. Final considerations. 5.4. Quotients -- 6. D-boundedness and D-compactness. 6.1. The probabilistic radius. 6.2. Boundedness in PN spaces. 6.3. Total boundedness. 6.4. D-compact sets in PN spaces. 6.5. Finite dimensional PN spaces -- 7. Normability. 7.1. Normability of Serstnev spaces. 7.2. Other cases. 7.3. Normability of PN spaces. 7.4. Open questions -- 8. Invariant and semi-invariant PN spaces. 8.1. Invariance and semi-invariance. 8.2. New class of PN spaces. 8.3. Open questions -- 9. Linear operators. 9.1. Boundedness of linear operators. 9.2. Classes of linear operators. 9.3. Probabilistic norms for linear operators. 9.4. Completeness results. 9.5. Families of linear operators -- 10. Stability of some functional equations in PN spaces. 10.1. Mouchtari-Serstnev theorem. 10.2. Stability of a functional equation in PN spaces. 10.3. The additive Cauchy functional equation in RN spaces: Stability. 10.4. Stability in the quartic functional equation in RN spaces. 10.5. A functional equation in Menger PN spaces -- 11. Menger's 2-probabilistic Normed spaces. 11.1. Accretive operators in 2-PN spaces. 11.2. Convex sets in 2-PN spaces. 11.3. Compactness and boundedness in 2-PN spaces. 11.4. D-boundedness in 2-PN spaces. |
| ctrlnum | (OCoLC)890146540 |
| dewey-full | 515/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.73 |
| dewey-search | 515/.73 |
| dewey-sort | 3515 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06299cam a2200553 i 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn890146540</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr mn|||||||||</controlfield><controlfield tag="008">140908t20142014nju ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">rda</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">IDEBK</subfield><subfield code="d">CDX</subfield><subfield code="d">OTZ</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OSU</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">OSU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">COO</subfield><subfield code="d">VTS</subfield><subfield code="d">STF</subfield><subfield code="d">LEAUB</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">SXB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781783264698</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1783264691</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9781783264681</subfield><subfield code="q">(alk. paper)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">1783264683</subfield><subfield code="q">(alk. paper)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)890146540</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA322.2</subfield><subfield code="b">.L38 2014eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">005000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">034000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515/.73</subfield><subfield code="2">23</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lafuerza Guillén, Bernardo,</subfield><subfield code="e">author.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Probabilistic normed spaces /</subfield><subfield code="c">Bernardo Lafuerza Guillén, Universidad de Almeria, Spain, Panackal Harikrishnan, Manipal Institute of Technology (MIT Manipal), India.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Hackensack, NJ :</subfield><subfield code="b">Imperial College Press,</subfield><subfield code="c">[2014]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2014</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xi, 220 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book provides a comprehensive foundation in Probabilistic Normed (PN) spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A.N. Serstnev in the early 1960s as a response to problems of best approximations in statistics. The theory was revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who provided a new, wider definition of a PN space which quickly became the standard adopted by all researchers. This book is the first wholly up-to-date and thorough investigation of the properties, uses and applications of PN spaces, based on the standard definition. Topics covered include: What are PN spaces? The topology of PN spaces. Probabilistic norms and convergence. Products and quotients of PN spaces. D-boundedness and D-compactness. Normability. Invariant and semi-invariant PN spaces. Linear operators. Stability of some functional equations in PN spaces. Menger's 2-probabilistic normed spaces. The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equations. This introduction will therefore have broad relevance across mathematical and statistical research, especially those working in probabilistic functional analysis and probabilistic geometry.</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">1. Preliminaries. 1.1. Probability spaces. 1.2. Distribution functions. 1.3. The space of distance of distribution functions. 1.4. Copulas. 1.5. Triangular norms. 1.6. Triangle functions. 1.7. Multiplications. 1.8. Probabilistic metric spaces. 1.9. L[symbol] and Orlicz spaces. 1.10. Domination. 1.11. Duality -- 2. Probabilistic Normed spaces. 2.1. Probabilistic Normed spaces. 2.2. 1993: PN spaces redefined. 2.3. Special classes of PN spaces. 2.4. [symbol]-simple spaces. 2.5. EN spaces. 2.6. Probabilistic inner product spaces. 2.7. Open questions -- 3. The topology of PN spaces. 3.1. The topology of a PN space. 3.2. The uniform continuity of the probabilistic norm. 3.3. A PN space as a topological vector space. 3.4. Completion of PN spaces. 3.5. Probabilistic metrization of generalized topologies. 3.6. TIGT induced by probabilistic norms -- 4. Probabilistic norms and convergence. 4.1. The L[symbol] and Orlicz norms. 4.2. Convergence of random variables -- 5. Products and quotients of PN spaces. 5.1. Finite products. 5.2. Countable products of PN spaces. 5.3. Final considerations. 5.4. Quotients -- 6. D-boundedness and D-compactness. 6.1. The probabilistic radius. 6.2. Boundedness in PN spaces. 6.3. Total boundedness. 6.4. D-compact sets in PN spaces. 6.5. Finite dimensional PN spaces -- 7. Normability. 7.1. Normability of Serstnev spaces. 7.2. Other cases. 7.3. Normability of PN spaces. 7.4. Open questions -- 8. Invariant and semi-invariant PN spaces. 8.1. Invariance and semi-invariance. 8.2. New class of PN spaces. 8.3. Open questions -- 9. Linear operators. 9.1. Boundedness of linear operators. 9.2. Classes of linear operators. 9.3. Probabilistic norms for linear operators. 9.4. Completeness results. 9.5. Families of linear operators -- 10. Stability of some functional equations in PN spaces. 10.1. Mouchtari-Serstnev theorem. 10.2. Stability of a functional equation in PN spaces. 10.3. The additive Cauchy functional equation in RN spaces: Stability. 10.4. Stability in the quartic functional equation in RN spaces. 10.5. A functional equation in Menger PN spaces -- 11. Menger's 2-probabilistic Normed spaces. 11.1. Accretive operators in 2-PN spaces. 11.2. Convex sets in 2-PN spaces. 11.3. Compactness and boundedness in 2-PN spaces. 11.4. D-boundedness in 2-PN spaces.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Normed linear spaces.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85092434</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Espaces linéaires normés.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Calculus.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Mathematical Analysis.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Normed linear spaces</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Harikrishnan, Panackal,</subfield><subfield code="e">author.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjG88kmjDG6c4vB9qMwgrq</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2014026214</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Probabilistic normed spaces (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGxWQKQ4ycYt83X3tDfb7d</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Lafuerza Guillén, Bernardo.</subfield><subfield code="t">Probabilistic normed spaces</subfield><subfield code="z">9781783264681</subfield><subfield code="w">(DLC) 2014018361</subfield><subfield code="w">(OCoLC)879553040</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=839691</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH27083574</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Coutts Information Services</subfield><subfield code="b">COUT</subfield><subfield code="n">29748685</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">839691</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">cis29748685</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">12058368</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn890146540 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:26:12Z |
| institution | BVB |
| isbn | 9781783264698 1783264691 |
| language | English |
| oclc_num | 890146540 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 220 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Imperial College Press, |
| record_format | marc |
| spelling | Lafuerza Guillén, Bernardo, author. Probabilistic normed spaces / Bernardo Lafuerza Guillén, Universidad de Almeria, Spain, Panackal Harikrishnan, Manipal Institute of Technology (MIT Manipal), India. Hackensack, NJ : Imperial College Press, [2014] ©2014 1 online resource (xi, 220 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier This book provides a comprehensive foundation in Probabilistic Normed (PN) spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A.N. Serstnev in the early 1960s as a response to problems of best approximations in statistics. The theory was revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who provided a new, wider definition of a PN space which quickly became the standard adopted by all researchers. This book is the first wholly up-to-date and thorough investigation of the properties, uses and applications of PN spaces, based on the standard definition. Topics covered include: What are PN spaces? The topology of PN spaces. Probabilistic norms and convergence. Products and quotients of PN spaces. D-boundedness and D-compactness. Normability. Invariant and semi-invariant PN spaces. Linear operators. Stability of some functional equations in PN spaces. Menger's 2-probabilistic normed spaces. The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equations. This introduction will therefore have broad relevance across mathematical and statistical research, especially those working in probabilistic functional analysis and probabilistic geometry. Includes bibliographical references and index. 1. Preliminaries. 1.1. Probability spaces. 1.2. Distribution functions. 1.3. The space of distance of distribution functions. 1.4. Copulas. 1.5. Triangular norms. 1.6. Triangle functions. 1.7. Multiplications. 1.8. Probabilistic metric spaces. 1.9. L[symbol] and Orlicz spaces. 1.10. Domination. 1.11. Duality -- 2. Probabilistic Normed spaces. 2.1. Probabilistic Normed spaces. 2.2. 1993: PN spaces redefined. 2.3. Special classes of PN spaces. 2.4. [symbol]-simple spaces. 2.5. EN spaces. 2.6. Probabilistic inner product spaces. 2.7. Open questions -- 3. The topology of PN spaces. 3.1. The topology of a PN space. 3.2. The uniform continuity of the probabilistic norm. 3.3. A PN space as a topological vector space. 3.4. Completion of PN spaces. 3.5. Probabilistic metrization of generalized topologies. 3.6. TIGT induced by probabilistic norms -- 4. Probabilistic norms and convergence. 4.1. The L[symbol] and Orlicz norms. 4.2. Convergence of random variables -- 5. Products and quotients of PN spaces. 5.1. Finite products. 5.2. Countable products of PN spaces. 5.3. Final considerations. 5.4. Quotients -- 6. D-boundedness and D-compactness. 6.1. The probabilistic radius. 6.2. Boundedness in PN spaces. 6.3. Total boundedness. 6.4. D-compact sets in PN spaces. 6.5. Finite dimensional PN spaces -- 7. Normability. 7.1. Normability of Serstnev spaces. 7.2. Other cases. 7.3. Normability of PN spaces. 7.4. Open questions -- 8. Invariant and semi-invariant PN spaces. 8.1. Invariance and semi-invariance. 8.2. New class of PN spaces. 8.3. Open questions -- 9. Linear operators. 9.1. Boundedness of linear operators. 9.2. Classes of linear operators. 9.3. Probabilistic norms for linear operators. 9.4. Completeness results. 9.5. Families of linear operators -- 10. Stability of some functional equations in PN spaces. 10.1. Mouchtari-Serstnev theorem. 10.2. Stability of a functional equation in PN spaces. 10.3. The additive Cauchy functional equation in RN spaces: Stability. 10.4. Stability in the quartic functional equation in RN spaces. 10.5. A functional equation in Menger PN spaces -- 11. Menger's 2-probabilistic Normed spaces. 11.1. Accretive operators in 2-PN spaces. 11.2. Convex sets in 2-PN spaces. 11.3. Compactness and boundedness in 2-PN spaces. 11.4. D-boundedness in 2-PN spaces. Print version record. Normed linear spaces. http://id.loc.gov/authorities/subjects/sh85092434 Espaces linéaires normés. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Normed linear spaces fast Harikrishnan, Panackal, author. https://id.oclc.org/worldcat/entity/E39PCjG88kmjDG6c4vB9qMwgrq http://id.loc.gov/authorities/names/n2014026214 has work: Probabilistic normed spaces (Text) https://id.oclc.org/worldcat/entity/E39PCGxWQKQ4ycYt83X3tDfb7d https://id.oclc.org/worldcat/ontology/hasWork Print version: Lafuerza Guillén, Bernardo. Probabilistic normed spaces 9781783264681 (DLC) 2014018361 (OCoLC)879553040 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=839691 Volltext |
| spellingShingle | Lafuerza Guillén, Bernardo Harikrishnan, Panackal Probabilistic normed spaces / 1. Preliminaries. 1.1. Probability spaces. 1.2. Distribution functions. 1.3. The space of distance of distribution functions. 1.4. Copulas. 1.5. Triangular norms. 1.6. Triangle functions. 1.7. Multiplications. 1.8. Probabilistic metric spaces. 1.9. L[symbol] and Orlicz spaces. 1.10. Domination. 1.11. Duality -- 2. Probabilistic Normed spaces. 2.1. Probabilistic Normed spaces. 2.2. 1993: PN spaces redefined. 2.3. Special classes of PN spaces. 2.4. [symbol]-simple spaces. 2.5. EN spaces. 2.6. Probabilistic inner product spaces. 2.7. Open questions -- 3. The topology of PN spaces. 3.1. The topology of a PN space. 3.2. The uniform continuity of the probabilistic norm. 3.3. A PN space as a topological vector space. 3.4. Completion of PN spaces. 3.5. Probabilistic metrization of generalized topologies. 3.6. TIGT induced by probabilistic norms -- 4. Probabilistic norms and convergence. 4.1. The L[symbol] and Orlicz norms. 4.2. Convergence of random variables -- 5. Products and quotients of PN spaces. 5.1. Finite products. 5.2. Countable products of PN spaces. 5.3. Final considerations. 5.4. Quotients -- 6. D-boundedness and D-compactness. 6.1. The probabilistic radius. 6.2. Boundedness in PN spaces. 6.3. Total boundedness. 6.4. D-compact sets in PN spaces. 6.5. Finite dimensional PN spaces -- 7. Normability. 7.1. Normability of Serstnev spaces. 7.2. Other cases. 7.3. Normability of PN spaces. 7.4. Open questions -- 8. Invariant and semi-invariant PN spaces. 8.1. Invariance and semi-invariance. 8.2. New class of PN spaces. 8.3. Open questions -- 9. Linear operators. 9.1. Boundedness of linear operators. 9.2. Classes of linear operators. 9.3. Probabilistic norms for linear operators. 9.4. Completeness results. 9.5. Families of linear operators -- 10. Stability of some functional equations in PN spaces. 10.1. Mouchtari-Serstnev theorem. 10.2. Stability of a functional equation in PN spaces. 10.3. The additive Cauchy functional equation in RN spaces: Stability. 10.4. Stability in the quartic functional equation in RN spaces. 10.5. A functional equation in Menger PN spaces -- 11. Menger's 2-probabilistic Normed spaces. 11.1. Accretive operators in 2-PN spaces. 11.2. Convex sets in 2-PN spaces. 11.3. Compactness and boundedness in 2-PN spaces. 11.4. D-boundedness in 2-PN spaces. Normed linear spaces. http://id.loc.gov/authorities/subjects/sh85092434 Espaces linéaires normés. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Normed linear spaces fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85092434 |
| title | Probabilistic normed spaces / |
| title_auth | Probabilistic normed spaces / |
| title_exact_search | Probabilistic normed spaces / |
| title_full | Probabilistic normed spaces / Bernardo Lafuerza Guillén, Universidad de Almeria, Spain, Panackal Harikrishnan, Manipal Institute of Technology (MIT Manipal), India. |
| title_fullStr | Probabilistic normed spaces / Bernardo Lafuerza Guillén, Universidad de Almeria, Spain, Panackal Harikrishnan, Manipal Institute of Technology (MIT Manipal), India. |
| title_full_unstemmed | Probabilistic normed spaces / Bernardo Lafuerza Guillén, Universidad de Almeria, Spain, Panackal Harikrishnan, Manipal Institute of Technology (MIT Manipal), India. |
| title_short | Probabilistic normed spaces / |
| title_sort | probabilistic normed spaces |
| topic | Normed linear spaces. http://id.loc.gov/authorities/subjects/sh85092434 Espaces linéaires normés. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Normed linear spaces fast |
| topic_facet | Normed linear spaces. Espaces linéaires normés. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Normed linear spaces |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=839691 |
| work_keys_str_mv | AT lafuerzaguillenbernardo probabilisticnormedspaces AT harikrishnanpanackal probabilisticnormedspaces |