Introduction to gauge integrals /:
This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an un...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
©2001.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces. A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc. |
| Beschreibung: | 1 online resource (x, 157 pages) |
| Bibliographie: | Includes bibliographical references (pages 149-153) and index. |
| ISBN: | 9789812810656 981281065X 1281956317 9781281956316 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn268993106 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 081105s2001 si ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d OCLCQ |d UBY |d IDEBK |d E7B |d OCLCQ |d OCLCF |d I9W |d NLGGC |d DKDLA |d EBLCP |d DEBSZ |d OCLCQ |d YDXCP |d OCLCQ |d AZK |d LOA |d JBG |d AGLDB |d COCUF |d MOR |d CCO |d PIFAG |d VGM |d ZCU |d OCLCQ |d MERUC |d OCLCQ |d U3W |d STF |d WRM |d VTS |d NRAMU |d ICG |d INT |d VT2 |d AU@ |d OCLCQ |d WYU |d TKN |d OCLCQ |d LEAUB |d DKC |d OCLCQ |d UKAHL |d OCLCQ |d AJS |d OCLCO |d OCLCQ |d OCLCO |d OCLCL |d SXB |d OCLKB |d OCLCQ | ||
| 019 | |a 505149559 |a 646768290 |a 764499254 |a 815755944 |a 961529404 |a 962725445 |a 1058739550 |a 1430179936 | ||
| 020 | |a 9789812810656 |q (electronic bk.) | ||
| 020 | |a 981281065X |q (electronic bk.) | ||
| 020 | |a 1281956317 | ||
| 020 | |a 9781281956316 | ||
| 020 | |z 9789810242398 | ||
| 020 | |z 9810242395 |q (alk. paper) | ||
| 035 | |a (OCoLC)268993106 |z (OCoLC)505149559 |z (OCoLC)646768290 |z (OCoLC)764499254 |z (OCoLC)815755944 |z (OCoLC)961529404 |z (OCoLC)962725445 |z (OCoLC)1058739550 |z (OCoLC)1430179936 | ||
| 050 | 4 | |a QA311 |b .S88 2001eb | |
| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 072 | 7 | |a PBK |2 bicssc | |
| 082 | 7 | |a 515/.43 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Swartz, Charles, |d 1938- |1 https://id.oclc.org/worldcat/entity/E39PBJbWrTbV8QTKgR6dhYwgrq |0 http://id.loc.gov/authorities/names/n84221175 | |
| 245 | 1 | 0 | |a Introduction to gauge integrals / |c Charles Swartz. |
| 246 | 3 | 0 | |a Gauge integrals |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c ©2001. | ||
| 300 | |a 1 online resource (x, 157 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (pages 149-153) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 1. Introduction to the gauge or Henstock-Kurzweil integral -- 2. Basic properties of the gauge integral -- 3. Henstock's lemma and improper integrals -- 4. The gauge integral over unbounded intervals -- 5. Convergence theorems -- 6. Integration over more general sets: Lebesgue measure -- 7. The space of gauge integrable functions -- 8. Multiple integrals and Fubini's theorem -- 9. The McShane integral. 9.1. Definition and basic properties. 9.2. Convergence theorems. 9.3. Integrability of products and integration by parts. 9.4. More general convergence theorems. 9.5. The space of McShane integrable functions. 9.6. Multiple integrals and Fubini's theorem -- 10. McShane integrability is equivalent to absolute Henstock-Kurzweil integrability. | |
| 520 | |a This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces. A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc. | ||
| 650 | 0 | |a Henstock-Kurzweil integral. |0 http://id.loc.gov/authorities/subjects/sh86004388 | |
| 650 | 0 | |a McShane integral. |0 http://id.loc.gov/authorities/subjects/sh2002009945 | |
| 650 | 6 | |a Intégrale de Kurzweil-Henstock. | |
| 650 | 6 | |a Intégrale de McShane. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Henstock-Kurzweil integral |2 fast | |
| 650 | 7 | |a McShane integral |2 fast | |
| 758 | |i has work: |a Introduction to gauge integrals (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGyCPtCcdWXCbhBmtJyB8y |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Swartz, Charles, 1938- |t Introduction to gauge integrals. |d Singapore ; River Edge, NJ : World Scientific, ©2001 |z 9810242395 |z 9789810242398 |w (DLC) 00068521 |w (OCoLC)45506028 |
| 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=235917 |3 Volltext |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH24685565 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL1681611 | ||
| 938 | |a ebrary |b EBRY |n ebr10255504 | ||
| 938 | |a EBSCOhost |b EBSC |n 235917 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 195631 | ||
| 938 | |a YBP Library Services |b YANK |n 2915232 | ||
| 938 | |b OCKB |z perlego.catalogue,702221d6-5a41-446e-9f6a-d0616d58628e-emi | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn268993106 |
|---|---|
| _version_ | 1816881679703212033 |
| adam_text | |
| any_adam_object | |
| author | Swartz, Charles, 1938- |
| author_GND | http://id.loc.gov/authorities/names/n84221175 |
| author_facet | Swartz, Charles, 1938- |
| author_role | |
| author_sort | Swartz, Charles, 1938- |
| author_variant | c s cs |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA311 |
| callnumber-raw | QA311 .S88 2001eb |
| callnumber-search | QA311 .S88 2001eb |
| callnumber-sort | QA 3311 S88 42001EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 1. Introduction to the gauge or Henstock-Kurzweil integral -- 2. Basic properties of the gauge integral -- 3. Henstock's lemma and improper integrals -- 4. The gauge integral over unbounded intervals -- 5. Convergence theorems -- 6. Integration over more general sets: Lebesgue measure -- 7. The space of gauge integrable functions -- 8. Multiple integrals and Fubini's theorem -- 9. The McShane integral. 9.1. Definition and basic properties. 9.2. Convergence theorems. 9.3. Integrability of products and integration by parts. 9.4. More general convergence theorems. 9.5. The space of McShane integrable functions. 9.6. Multiple integrals and Fubini's theorem -- 10. McShane integrability is equivalent to absolute Henstock-Kurzweil integrability. |
| ctrlnum | (OCoLC)268993106 |
| dewey-full | 515/.43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.43 |
| dewey-search | 515/.43 |
| dewey-sort | 3515 243 |
| 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>04728cam a2200649 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn268993106</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">081105s2001 si ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UBY</subfield><subfield code="d">IDEBK</subfield><subfield code="d">E7B</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">I9W</subfield><subfield code="d">NLGGC</subfield><subfield code="d">DKDLA</subfield><subfield code="d">EBLCP</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AZK</subfield><subfield code="d">LOA</subfield><subfield code="d">JBG</subfield><subfield code="d">AGLDB</subfield><subfield code="d">COCUF</subfield><subfield code="d">MOR</subfield><subfield code="d">CCO</subfield><subfield code="d">PIFAG</subfield><subfield code="d">VGM</subfield><subfield code="d">ZCU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">MERUC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">U3W</subfield><subfield code="d">STF</subfield><subfield code="d">WRM</subfield><subfield code="d">VTS</subfield><subfield code="d">NRAMU</subfield><subfield code="d">ICG</subfield><subfield code="d">INT</subfield><subfield code="d">VT2</subfield><subfield code="d">AU@</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WYU</subfield><subfield code="d">TKN</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">LEAUB</subfield><subfield code="d">DKC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AJS</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">OCLKB</subfield><subfield code="d">OCLCQ</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">505149559</subfield><subfield code="a">646768290</subfield><subfield code="a">764499254</subfield><subfield code="a">815755944</subfield><subfield code="a">961529404</subfield><subfield code="a">962725445</subfield><subfield code="a">1058739550</subfield><subfield code="a">1430179936</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812810656</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">981281065X</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1281956317</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781281956316</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9789810242398</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9810242395</subfield><subfield code="q">(alk. paper)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)268993106</subfield><subfield code="z">(OCoLC)505149559</subfield><subfield code="z">(OCoLC)646768290</subfield><subfield code="z">(OCoLC)764499254</subfield><subfield code="z">(OCoLC)815755944</subfield><subfield code="z">(OCoLC)961529404</subfield><subfield code="z">(OCoLC)962725445</subfield><subfield code="z">(OCoLC)1058739550</subfield><subfield code="z">(OCoLC)1430179936</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA311</subfield><subfield code="b">.S88 2001eb</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="072" ind1=" " ind2="7"><subfield code="a">PBK</subfield><subfield code="2">bicssc</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515/.43</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Swartz, Charles,</subfield><subfield code="d">1938-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJbWrTbV8QTKgR6dhYwgrq</subfield><subfield code="0">http://id.loc.gov/authorities/names/n84221175</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to gauge integrals /</subfield><subfield code="c">Charles Swartz.</subfield></datafield><datafield tag="246" ind1="3" ind2="0"><subfield code="a">Gauge integrals</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Singapore ;</subfield><subfield code="a">River Edge, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">©2001.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (x, 157 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="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 149-153) and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">1. Introduction to the gauge or Henstock-Kurzweil integral -- 2. Basic properties of the gauge integral -- 3. Henstock's lemma and improper integrals -- 4. The gauge integral over unbounded intervals -- 5. Convergence theorems -- 6. Integration over more general sets: Lebesgue measure -- 7. The space of gauge integrable functions -- 8. Multiple integrals and Fubini's theorem -- 9. The McShane integral. 9.1. Definition and basic properties. 9.2. Convergence theorems. 9.3. Integrability of products and integration by parts. 9.4. More general convergence theorems. 9.5. The space of McShane integrable functions. 9.6. Multiple integrals and Fubini's theorem -- 10. McShane integrability is equivalent to absolute Henstock-Kurzweil integrability.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces. A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Henstock-Kurzweil integral.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh86004388</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">McShane integral.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh2002009945</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Intégrale de Kurzweil-Henstock.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Intégrale de McShane.</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">Henstock-Kurzweil integral</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">McShane integral</subfield><subfield code="2">fast</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Introduction to gauge integrals (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGyCPtCcdWXCbhBmtJyB8y</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">Swartz, Charles, 1938-</subfield><subfield code="t">Introduction to gauge integrals.</subfield><subfield code="d">Singapore ; River Edge, NJ : World Scientific, ©2001</subfield><subfield code="z">9810242395</subfield><subfield code="z">9789810242398</subfield><subfield code="w">(DLC) 00068521</subfield><subfield code="w">(OCoLC)45506028</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=235917</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">AH24685565</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL1681611</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10255504</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">235917</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">195631</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2915232</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="b">OCKB</subfield><subfield code="z">perlego.catalogue,702221d6-5a41-446e-9f6a-d0616d58628e-emi</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-ocn268993106 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:33Z |
| institution | BVB |
| isbn | 9789812810656 981281065X 1281956317 9781281956316 |
| language | English |
| oclc_num | 268993106 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (x, 157 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Swartz, Charles, 1938- https://id.oclc.org/worldcat/entity/E39PBJbWrTbV8QTKgR6dhYwgrq http://id.loc.gov/authorities/names/n84221175 Introduction to gauge integrals / Charles Swartz. Gauge integrals Singapore ; River Edge, NJ : World Scientific, ©2001. 1 online resource (x, 157 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 149-153) and index. Print version record. 1. Introduction to the gauge or Henstock-Kurzweil integral -- 2. Basic properties of the gauge integral -- 3. Henstock's lemma and improper integrals -- 4. The gauge integral over unbounded intervals -- 5. Convergence theorems -- 6. Integration over more general sets: Lebesgue measure -- 7. The space of gauge integrable functions -- 8. Multiple integrals and Fubini's theorem -- 9. The McShane integral. 9.1. Definition and basic properties. 9.2. Convergence theorems. 9.3. Integrability of products and integration by parts. 9.4. More general convergence theorems. 9.5. The space of McShane integrable functions. 9.6. Multiple integrals and Fubini's theorem -- 10. McShane integrability is equivalent to absolute Henstock-Kurzweil integrability. This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces. A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc. Henstock-Kurzweil integral. http://id.loc.gov/authorities/subjects/sh86004388 McShane integral. http://id.loc.gov/authorities/subjects/sh2002009945 Intégrale de Kurzweil-Henstock. Intégrale de McShane. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Henstock-Kurzweil integral fast McShane integral fast has work: Introduction to gauge integrals (Text) https://id.oclc.org/worldcat/entity/E39PCGyCPtCcdWXCbhBmtJyB8y https://id.oclc.org/worldcat/ontology/hasWork Print version: Swartz, Charles, 1938- Introduction to gauge integrals. Singapore ; River Edge, NJ : World Scientific, ©2001 9810242395 9789810242398 (DLC) 00068521 (OCoLC)45506028 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235917 Volltext |
| spellingShingle | Swartz, Charles, 1938- Introduction to gauge integrals / 1. Introduction to the gauge or Henstock-Kurzweil integral -- 2. Basic properties of the gauge integral -- 3. Henstock's lemma and improper integrals -- 4. The gauge integral over unbounded intervals -- 5. Convergence theorems -- 6. Integration over more general sets: Lebesgue measure -- 7. The space of gauge integrable functions -- 8. Multiple integrals and Fubini's theorem -- 9. The McShane integral. 9.1. Definition and basic properties. 9.2. Convergence theorems. 9.3. Integrability of products and integration by parts. 9.4. More general convergence theorems. 9.5. The space of McShane integrable functions. 9.6. Multiple integrals and Fubini's theorem -- 10. McShane integrability is equivalent to absolute Henstock-Kurzweil integrability. Henstock-Kurzweil integral. http://id.loc.gov/authorities/subjects/sh86004388 McShane integral. http://id.loc.gov/authorities/subjects/sh2002009945 Intégrale de Kurzweil-Henstock. Intégrale de McShane. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Henstock-Kurzweil integral fast McShane integral fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh86004388 http://id.loc.gov/authorities/subjects/sh2002009945 |
| title | Introduction to gauge integrals / |
| title_alt | Gauge integrals |
| title_auth | Introduction to gauge integrals / |
| title_exact_search | Introduction to gauge integrals / |
| title_full | Introduction to gauge integrals / Charles Swartz. |
| title_fullStr | Introduction to gauge integrals / Charles Swartz. |
| title_full_unstemmed | Introduction to gauge integrals / Charles Swartz. |
| title_short | Introduction to gauge integrals / |
| title_sort | introduction to gauge integrals |
| topic | Henstock-Kurzweil integral. http://id.loc.gov/authorities/subjects/sh86004388 McShane integral. http://id.loc.gov/authorities/subjects/sh2002009945 Intégrale de Kurzweil-Henstock. Intégrale de McShane. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Henstock-Kurzweil integral fast McShane integral fast |
| topic_facet | Henstock-Kurzweil integral. McShane integral. Intégrale de Kurzweil-Henstock. Intégrale de McShane. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Henstock-Kurzweil integral McShane integral |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235917 |
| work_keys_str_mv | AT swartzcharles introductiontogaugeintegrals AT swartzcharles gaugeintegrals |