Nonmeasurable sets and functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier
2004
|
| Ausgabe: | 1st ed |
| Schriftenreihe: | North-Holland mathematics studies
195 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics: 1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces; 2. The theory of non-real-valued-measurable cardinals; 3. The theory of invariant (quasi-invariant) extensions of invariant (quasi-invariant) measures. These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions. highlights the importance of nonmeasurable sets (functions) for general measure extension problem. Deep connections of the topic with set theory, real analysis, infinite combinatorics, group theory and geometry of Euclidean spaces shown and underlined. self-contained and accessible for a wide audience of potential readers. Each chapter ends with exercises which provide valuable additional information about nonmeasurable sets and functions. Numerous open problems and questions Includes bibliographical references (p. 317-333) and index |
| Beschreibung: | 1 Online-Ressource (xi, 337 p.) |
| ISBN: | 9780444516268 0444516263 1423741846 9781423741848 0080479766 9780080479767 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042317244 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150129s2004 |||| o||u| ||||||eng d | ||
| 020 | |a 9780444516268 |9 978-0-444-51626-8 | ||
| 020 | |a 0444516263 |9 0-444-51626-3 | ||
| 020 | |a 1423741846 |c electronic bk. |9 1-4237-4184-6 | ||
| 020 | |a 9781423741848 |c electronic bk. |9 978-1-4237-4184-8 | ||
| 020 | |a 0080479766 |c electronic bk. |9 0-08-047976-6 | ||
| 020 | |a 9780080479767 |c electronic bk. |9 978-0-08-047976-7 | ||
| 035 | |a (ZDB-33-EBS)ocn162130131 | ||
| 035 | |a (OCoLC)162130131 | ||
| 035 | |a (DE-599)BVBBV042317244 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 | ||
| 082 | 0 | |a 515/.42 |2 22 | |
| 100 | 1 | |a Kharazishvili, A. B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonmeasurable sets and functions |c A.B. Kharazishvili |
| 250 | |a 1st ed | ||
| 264 | 1 | |a Amsterdam |b Elsevier |c 2004 | |
| 300 | |a 1 Online-Ressource (xi, 337 p.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a North-Holland mathematics studies |v 195 | |
| 500 | |a The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics: 1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces; 2. The theory of non-real-valued-measurable cardinals; 3. The theory of invariant (quasi-invariant) extensions of invariant (quasi-invariant) measures. These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . | ||
| 500 | |a Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions. highlights the importance of nonmeasurable sets (functions) for general measure extension problem. | ||
| 500 | |a Deep connections of the topic with set theory, real analysis, infinite combinatorics, group theory and geometry of Euclidean spaces shown and underlined. self-contained and accessible for a wide audience of potential readers. Each chapter ends with exercises which provide valuable additional information about nonmeasurable sets and functions. Numerous open problems and questions | ||
| 500 | |a Includes bibliographical references (p. 317-333) and index | ||
| 650 | 7 | |a MATHEMATICS / Calculus |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Mathematical Analysis |2 bisacsh | |
| 650 | 7 | |a Functional analysis |2 fast | |
| 650 | 7 | |a Measure theory |2 fast | |
| 650 | 7 | |a Set theory |2 fast | |
| 650 | 4 | |a Measure theory | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Set theory | |
| 856 | 4 | 0 | |u http://www.sciencedirect.com/science/book/9780444516268 |x Verlag |3 Volltext |
| 912 | |a ZDB-33-ESD |a ZDB-33-EBS | ||
| 940 | 1 | |q FAW_PDA_ESD | |
| 940 | 1 | |q FLA_PDA_ESD | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027754235 | ||
Datensatz im Suchindex
| _version_ | 1804152913481695233 |
|---|---|
| any_adam_object | |
| author | Kharazishvili, A. B. |
| author_facet | Kharazishvili, A. B. |
| author_role | aut |
| author_sort | Kharazishvili, A. B. |
| author_variant | a b k ab abk |
| building | Verbundindex |
| bvnumber | BV042317244 |
| collection | ZDB-33-ESD ZDB-33-EBS |
| ctrlnum | (ZDB-33-EBS)ocn162130131 (OCoLC)162130131 (DE-599)BVBBV042317244 |
| dewey-full | 515/.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.42 |
| dewey-search | 515/.42 |
| dewey-sort | 3515 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03862nmm a2200553zcb4500</leader><controlfield tag="001">BV042317244</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150129s2004 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780444516268</subfield><subfield code="9">978-0-444-51626-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0444516263</subfield><subfield code="9">0-444-51626-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1423741846</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">1-4237-4184-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781423741848</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-1-4237-4184-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0080479766</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">0-08-047976-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780080479767</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-0-08-047976-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-33-EBS)ocn162130131</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)162130131</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042317244</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.42</subfield><subfield code="2">22</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kharazishvili, A. B.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonmeasurable sets and functions</subfield><subfield code="c">A.B. Kharazishvili</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1st ed</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Amsterdam</subfield><subfield code="b">Elsevier</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xi, 337 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">North-Holland mathematics studies</subfield><subfield code="v">195</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics: 1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces; 2. The theory of non-real-valued-measurable cardinals; 3. The theory of invariant (quasi-invariant) extensions of invariant (quasi-invariant) measures. These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions. highlights the importance of nonmeasurable sets (functions) for general measure extension problem. </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Deep connections of the topic with set theory, real analysis, infinite combinatorics, group theory and geometry of Euclidean spaces shown and underlined. self-contained and accessible for a wide audience of potential readers. Each chapter ends with exercises which provide valuable additional information about nonmeasurable sets and functions. Numerous open problems and questions</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (p. 317-333) and index</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Calculus</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Mathematical Analysis</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Functional analysis</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Measure theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Set theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Measure theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Set theory</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.sciencedirect.com/science/book/9780444516268</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-33-ESD</subfield><subfield code="a">ZDB-33-EBS</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">FAW_PDA_ESD</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">FLA_PDA_ESD</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027754235</subfield></datafield></record></collection> |
| id | DE-604.BV042317244 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:16Z |
| institution | BVB |
| isbn | 9780444516268 0444516263 1423741846 9781423741848 0080479766 9780080479767 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027754235 |
| oclc_num | 162130131 |
| open_access_boolean | |
| owner | DE-1046 |
| owner_facet | DE-1046 |
| physical | 1 Online-Ressource (xi, 337 p.) |
| psigel | ZDB-33-ESD ZDB-33-EBS FAW_PDA_ESD FLA_PDA_ESD |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Elsevier |
| record_format | marc |
| series2 | North-Holland mathematics studies |
| spelling | Kharazishvili, A. B. Verfasser aut Nonmeasurable sets and functions A.B. Kharazishvili 1st ed Amsterdam Elsevier 2004 1 Online-Ressource (xi, 337 p.) txt rdacontent c rdamedia cr rdacarrier North-Holland mathematics studies 195 The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics: 1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces; 2. The theory of non-real-valued-measurable cardinals; 3. The theory of invariant (quasi-invariant) extensions of invariant (quasi-invariant) measures. These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions. highlights the importance of nonmeasurable sets (functions) for general measure extension problem. Deep connections of the topic with set theory, real analysis, infinite combinatorics, group theory and geometry of Euclidean spaces shown and underlined. self-contained and accessible for a wide audience of potential readers. Each chapter ends with exercises which provide valuable additional information about nonmeasurable sets and functions. Numerous open problems and questions Includes bibliographical references (p. 317-333) and index MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Functional analysis fast Measure theory fast Set theory fast Measure theory Functional analysis Set theory http://www.sciencedirect.com/science/book/9780444516268 Verlag Volltext |
| spellingShingle | Kharazishvili, A. B. Nonmeasurable sets and functions MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Functional analysis fast Measure theory fast Set theory fast Measure theory Functional analysis Set theory |
| title | Nonmeasurable sets and functions |
| title_auth | Nonmeasurable sets and functions |
| title_exact_search | Nonmeasurable sets and functions |
| title_full | Nonmeasurable sets and functions A.B. Kharazishvili |
| title_fullStr | Nonmeasurable sets and functions A.B. Kharazishvili |
| title_full_unstemmed | Nonmeasurable sets and functions A.B. Kharazishvili |
| title_short | Nonmeasurable sets and functions |
| title_sort | nonmeasurable sets and functions |
| topic | MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Functional analysis fast Measure theory fast Set theory fast Measure theory Functional analysis Set theory |
| topic_facet | MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Functional analysis Measure theory Set theory |
| url | http://www.sciencedirect.com/science/book/9780444516268 |
| work_keys_str_mv | AT kharazishviliab nonmeasurablesetsandfunctions |