Henstock-Kurzweil integration on Euclidean spaces /:
The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the...
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New Jersey :
World Scientific,
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| Schriftenreihe: | Series in real analysis ;
v. 12. |
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| Online-Zugang: | Volltext |
| Zusammenfassung: | The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus. |
| Beschreibung: | 1 online resource (ix, 314 pages). |
| Bibliographie: | Includes bibliographical references (pages 295-303) and index. |
| ISBN: | 9789814324595 9814324590 |
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| 100 | 1 | |a Lee, Tuo Yeong, |d 1967- |1 https://id.oclc.org/worldcat/entity/E39PCjy8CGYVrCVVcVkxWw4hh3 |0 http://id.loc.gov/authorities/names/no2011083170 | |
| 245 | 1 | 0 | |a Henstock-Kurzweil integration on Euclidean spaces / |c Lee Tuo Yeong. |
| 260 | |a New Jersey : |b World Scientific, |c ©2011. | ||
| 300 | |a 1 online resource (ix, 314 pages). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Series in real analysis ; |v v. 12 | |
| 504 | |a Includes bibliographical references (pages 295-303) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 1. The one-dimensional Henstock-Kurzweil integral. 1.1. Introduction and Cousin's lemma. 1.2. Definition of the Henstock-Kurzweil integral. 1.3. Simple properties. 1.4. Saks-Henstock lemma. 1.5. Notes and remarks -- 2. The multiple Henstock-Kurzweil integral. 2.1. Preliminaries. 2.2. The Henstock-Kurzweil integral. 2.3. Simple properties. 2.4. Saks-Henstock lemma. 2.5. Fubini's theorem. 2.6. Notes and remarks -- 3. Lebesgue integrable functions. 3.1. Introduction. 3.2. Some convergence theorems for Lebesgue integrals. 3.3. [symbol]-measurable sets. 3.4. A characterization of [symbol]-measurable sets. 3.5. [symbol]-measurable functions. 3.6. Vitali covering theorem. 3.7. Further properties of Lebesgue integrable functions. 3.8. The L[symbol] spaces. 3.9. Lebesgue's criterion for Riemann integrability. 3.10. Some characterizations of Lebesgue integrable functions. 3.11. Some results concerning one-dimensional Lebesgue integral. 3.12. Notes and remarks -- 4. Further properties of Henstock-Kurzweil integrable functions. 4.1. A necessary condition for Henstock-Kurzweil integrability. 4.2. A result of Kurzweil and Jarnik. 4.3. Some necessary and sufficient conditions for Henstock-Kurzweil integrability. 4.4. Harnack extension for one-dimensional Henstock-Kurzweil integrals. 4.5. Other results concerning one-dimensional Henstock-Kurzweil integral. 4.6. Notes and remarks -- 5. The Henstock variational measure. 5.1. Lebesgue outer measure. 5.2. Basic properties of the Henstock variational measure. 5.3. Another characterization of Lebesgue integrable functions. 5.4. A result of Kurzweil and Jarnik revisited. 5.5. A measure-theoretic characterization of the Henstock-Kurzweil integral. 5.6. Product variational measures. 5.7. Notes and remarks. | |
| 505 | 8 | |a 6. Multipliers for the Henstock-Kurzweil integral. 6.1. One-dimensional integration by parts. 6.2. On functions of bounded variation in the sense of Vitali. 6.3. The m-dimensional Riemann-Stieltjes integral. 6.4. A multiple integration by parts for the Henstock-Kurzweil integral. 6.5. Kurzweil's multiple integration by parts formula for the Henstock-Kurzweil integral. 6.6. Riesz representation theorems. 6.7. Characterization of multipliers for the Henstock-Kurzweil integral. 6.8. A Banach-Steinhaus theorem for the space of Henstock-Kurzweil integrable functions. 6.9. Notes and remarks -- 7. Some selected topics in trigonometric series. 7.1. A generalized Dirichlet test. 7.2. Fourier series. 7.3. Some examples of Fourier series. 7.4. Some Lebesgue integrability theorems for trigonometric series. 7.5. Boas' results. 7.6. On a result of Hardy and Littlewood concerning Fourier series. 7.7. Notes and remarks -- 8. Some applications of the Henstock-Kurzweil integral to double trigonometric series. 8.1. Regularly convergent double series. 8.2. Double Fourier series. 8.3. Some examples of double Fourier series. 8.4. A Lebesgue integrability theorem for double cosine series. 8.5. A Lebesgue integrability theorem for double sine series. 8.6. A convergence theorem for Henstock-Kurzweil integrals. 8.7. Applications to double Fourier series. 8.8. Another convergence theorem for Henstock-Kurzweil integrals. 8.9. A two-dimensional analogue of Boas' theorem. 8.10. A convergence theorem for double sine series. 8.11. Some open problems. 8.12. Notes and remarks. | |
| 520 | |a The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus. | ||
| 650 | 0 | |a Henstock-Kurzweil integral. |0 http://id.loc.gov/authorities/subjects/sh86004388 | |
| 650 | 0 | |a Lebesgue integral. |0 http://id.loc.gov/authorities/subjects/sh94008345 | |
| 650 | 0 | |a Calculus, Integral. |0 http://id.loc.gov/authorities/subjects/sh85018804 | |
| 650 | 6 | |a Intégrale de Kurzweil-Henstock. | |
| 650 | 6 | |a Intégrale de Lebesgue. | |
| 650 | 6 | |a Calcul intégral. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Calculus, Integral |2 fast | |
| 650 | 7 | |a Henstock-Kurzweil integral |2 fast | |
| 650 | 7 | |a Lebesgue integral |2 fast | |
| 758 | |i has work: |a Henstock-Kurzweil integration on Euclidean spaces (Work) |1 https://id.oclc.org/worldcat/entity/E39PCFC3KV6677B4fWg9M6vyh3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Lee, Tuo Yeong, 1967- |t Henstock-Kurzweil integration on Euclidean spaces. |d Singapore ; Hackensack, N.J. : World Scientific, ©2011 |z 9789814324588 |w (OCoLC)724966681 |
| 830 | 0 | |a Series in real analysis ; |v v. 12. |0 http://id.loc.gov/authorities/names/n88505405 | |
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| contents | 1. The one-dimensional Henstock-Kurzweil integral. 1.1. Introduction and Cousin's lemma. 1.2. Definition of the Henstock-Kurzweil integral. 1.3. Simple properties. 1.4. Saks-Henstock lemma. 1.5. Notes and remarks -- 2. The multiple Henstock-Kurzweil integral. 2.1. Preliminaries. 2.2. The Henstock-Kurzweil integral. 2.3. Simple properties. 2.4. Saks-Henstock lemma. 2.5. Fubini's theorem. 2.6. Notes and remarks -- 3. Lebesgue integrable functions. 3.1. Introduction. 3.2. Some convergence theorems for Lebesgue integrals. 3.3. [symbol]-measurable sets. 3.4. A characterization of [symbol]-measurable sets. 3.5. [symbol]-measurable functions. 3.6. Vitali covering theorem. 3.7. Further properties of Lebesgue integrable functions. 3.8. The L[symbol] spaces. 3.9. Lebesgue's criterion for Riemann integrability. 3.10. Some characterizations of Lebesgue integrable functions. 3.11. Some results concerning one-dimensional Lebesgue integral. 3.12. Notes and remarks -- 4. Further properties of Henstock-Kurzweil integrable functions. 4.1. A necessary condition for Henstock-Kurzweil integrability. 4.2. A result of Kurzweil and Jarnik. 4.3. Some necessary and sufficient conditions for Henstock-Kurzweil integrability. 4.4. Harnack extension for one-dimensional Henstock-Kurzweil integrals. 4.5. Other results concerning one-dimensional Henstock-Kurzweil integral. 4.6. Notes and remarks -- 5. The Henstock variational measure. 5.1. Lebesgue outer measure. 5.2. Basic properties of the Henstock variational measure. 5.3. Another characterization of Lebesgue integrable functions. 5.4. A result of Kurzweil and Jarnik revisited. 5.5. A measure-theoretic characterization of the Henstock-Kurzweil integral. 5.6. Product variational measures. 5.7. Notes and remarks. 6. Multipliers for the Henstock-Kurzweil integral. 6.1. One-dimensional integration by parts. 6.2. On functions of bounded variation in the sense of Vitali. 6.3. The m-dimensional Riemann-Stieltjes integral. 6.4. A multiple integration by parts for the Henstock-Kurzweil integral. 6.5. Kurzweil's multiple integration by parts formula for the Henstock-Kurzweil integral. 6.6. Riesz representation theorems. 6.7. Characterization of multipliers for the Henstock-Kurzweil integral. 6.8. A Banach-Steinhaus theorem for the space of Henstock-Kurzweil integrable functions. 6.9. Notes and remarks -- 7. Some selected topics in trigonometric series. 7.1. A generalized Dirichlet test. 7.2. Fourier series. 7.3. Some examples of Fourier series. 7.4. Some Lebesgue integrability theorems for trigonometric series. 7.5. Boas' results. 7.6. On a result of Hardy and Littlewood concerning Fourier series. 7.7. Notes and remarks -- 8. Some applications of the Henstock-Kurzweil integral to double trigonometric series. 8.1. Regularly convergent double series. 8.2. Double Fourier series. 8.3. Some examples of double Fourier series. 8.4. A Lebesgue integrability theorem for double cosine series. 8.5. A Lebesgue integrability theorem for double sine series. 8.6. A convergence theorem for Henstock-Kurzweil integrals. 8.7. Applications to double Fourier series. 8.8. Another convergence theorem for Henstock-Kurzweil integrals. 8.9. A two-dimensional analogue of Boas' theorem. 8.10. A convergence theorem for double sine series. 8.11. Some open problems. 8.12. Notes and remarks. |
| ctrlnum | (OCoLC)754793038 |
| dewey-full | 515.4/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.4/3 |
| dewey-search | 515.4/3 |
| dewey-sort | 3515.4 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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The one-dimensional Henstock-Kurzweil integral. 1.1. Introduction and Cousin's lemma. 1.2. Definition of the Henstock-Kurzweil integral. 1.3. Simple properties. 1.4. Saks-Henstock lemma. 1.5. Notes and remarks -- 2. The multiple Henstock-Kurzweil integral. 2.1. Preliminaries. 2.2. The Henstock-Kurzweil integral. 2.3. Simple properties. 2.4. Saks-Henstock lemma. 2.5. Fubini's theorem. 2.6. Notes and remarks -- 3. Lebesgue integrable functions. 3.1. Introduction. 3.2. Some convergence theorems for Lebesgue integrals. 3.3. [symbol]-measurable sets. 3.4. A characterization of [symbol]-measurable sets. 3.5. [symbol]-measurable functions. 3.6. Vitali covering theorem. 3.7. Further properties of Lebesgue integrable functions. 3.8. The L[symbol] spaces. 3.9. Lebesgue's criterion for Riemann integrability. 3.10. Some characterizations of Lebesgue integrable functions. 3.11. Some results concerning one-dimensional Lebesgue integral. 3.12. Notes and remarks -- 4. Further properties of Henstock-Kurzweil integrable functions. 4.1. A necessary condition for Henstock-Kurzweil integrability. 4.2. A result of Kurzweil and Jarnik. 4.3. Some necessary and sufficient conditions for Henstock-Kurzweil integrability. 4.4. Harnack extension for one-dimensional Henstock-Kurzweil integrals. 4.5. Other results concerning one-dimensional Henstock-Kurzweil integral. 4.6. Notes and remarks -- 5. The Henstock variational measure. 5.1. Lebesgue outer measure. 5.2. Basic properties of the Henstock variational measure. 5.3. Another characterization of Lebesgue integrable functions. 5.4. A result of Kurzweil and Jarnik revisited. 5.5. A measure-theoretic characterization of the Henstock-Kurzweil integral. 5.6. Product variational measures. 5.7. Notes and remarks.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6. Multipliers for the Henstock-Kurzweil integral. 6.1. One-dimensional integration by parts. 6.2. On functions of bounded variation in the sense of Vitali. 6.3. The m-dimensional Riemann-Stieltjes integral. 6.4. A multiple integration by parts for the Henstock-Kurzweil integral. 6.5. Kurzweil's multiple integration by parts formula for the Henstock-Kurzweil integral. 6.6. Riesz representation theorems. 6.7. Characterization of multipliers for the Henstock-Kurzweil integral. 6.8. A Banach-Steinhaus theorem for the space of Henstock-Kurzweil integrable functions. 6.9. Notes and remarks -- 7. Some selected topics in trigonometric series. 7.1. A generalized Dirichlet test. 7.2. Fourier series. 7.3. Some examples of Fourier series. 7.4. Some Lebesgue integrability theorems for trigonometric series. 7.5. Boas' results. 7.6. On a result of Hardy and Littlewood concerning Fourier series. 7.7. Notes and remarks -- 8. Some applications of the Henstock-Kurzweil integral to double trigonometric series. 8.1. Regularly convergent double series. 8.2. Double Fourier series. 8.3. Some examples of double Fourier series. 8.4. A Lebesgue integrability theorem for double cosine series. 8.5. A Lebesgue integrability theorem for double sine series. 8.6. A convergence theorem for Henstock-Kurzweil integrals. 8.7. Applications to double Fourier series. 8.8. Another convergence theorem for Henstock-Kurzweil integrals. 8.9. A two-dimensional analogue of Boas' theorem. 8.10. A convergence theorem for double sine series. 8.11. Some open problems. 8.12. Notes and remarks.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. 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| id | ZDB-4-EBA-ocn754793038 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:01Z |
| institution | BVB |
| isbn | 9789814324595 9814324590 |
| language | English |
| oclc_num | 754793038 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (ix, 314 pages). |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific, |
| record_format | marc |
| series | Series in real analysis ; |
| series2 | Series in real analysis ; |
| spelling | Lee, Tuo Yeong, 1967- https://id.oclc.org/worldcat/entity/E39PCjy8CGYVrCVVcVkxWw4hh3 http://id.loc.gov/authorities/names/no2011083170 Henstock-Kurzweil integration on Euclidean spaces / Lee Tuo Yeong. New Jersey : World Scientific, ©2011. 1 online resource (ix, 314 pages). text txt rdacontent computer c rdamedia online resource cr rdacarrier Series in real analysis ; v. 12 Includes bibliographical references (pages 295-303) and index. Print version record. 1. The one-dimensional Henstock-Kurzweil integral. 1.1. Introduction and Cousin's lemma. 1.2. Definition of the Henstock-Kurzweil integral. 1.3. Simple properties. 1.4. Saks-Henstock lemma. 1.5. Notes and remarks -- 2. The multiple Henstock-Kurzweil integral. 2.1. Preliminaries. 2.2. The Henstock-Kurzweil integral. 2.3. Simple properties. 2.4. Saks-Henstock lemma. 2.5. Fubini's theorem. 2.6. Notes and remarks -- 3. Lebesgue integrable functions. 3.1. Introduction. 3.2. Some convergence theorems for Lebesgue integrals. 3.3. [symbol]-measurable sets. 3.4. A characterization of [symbol]-measurable sets. 3.5. [symbol]-measurable functions. 3.6. Vitali covering theorem. 3.7. Further properties of Lebesgue integrable functions. 3.8. The L[symbol] spaces. 3.9. Lebesgue's criterion for Riemann integrability. 3.10. Some characterizations of Lebesgue integrable functions. 3.11. Some results concerning one-dimensional Lebesgue integral. 3.12. Notes and remarks -- 4. Further properties of Henstock-Kurzweil integrable functions. 4.1. A necessary condition for Henstock-Kurzweil integrability. 4.2. A result of Kurzweil and Jarnik. 4.3. Some necessary and sufficient conditions for Henstock-Kurzweil integrability. 4.4. Harnack extension for one-dimensional Henstock-Kurzweil integrals. 4.5. Other results concerning one-dimensional Henstock-Kurzweil integral. 4.6. Notes and remarks -- 5. The Henstock variational measure. 5.1. Lebesgue outer measure. 5.2. Basic properties of the Henstock variational measure. 5.3. Another characterization of Lebesgue integrable functions. 5.4. A result of Kurzweil and Jarnik revisited. 5.5. A measure-theoretic characterization of the Henstock-Kurzweil integral. 5.6. Product variational measures. 5.7. Notes and remarks. 6. Multipliers for the Henstock-Kurzweil integral. 6.1. One-dimensional integration by parts. 6.2. On functions of bounded variation in the sense of Vitali. 6.3. The m-dimensional Riemann-Stieltjes integral. 6.4. A multiple integration by parts for the Henstock-Kurzweil integral. 6.5. Kurzweil's multiple integration by parts formula for the Henstock-Kurzweil integral. 6.6. Riesz representation theorems. 6.7. Characterization of multipliers for the Henstock-Kurzweil integral. 6.8. A Banach-Steinhaus theorem for the space of Henstock-Kurzweil integrable functions. 6.9. Notes and remarks -- 7. Some selected topics in trigonometric series. 7.1. A generalized Dirichlet test. 7.2. Fourier series. 7.3. Some examples of Fourier series. 7.4. Some Lebesgue integrability theorems for trigonometric series. 7.5. Boas' results. 7.6. On a result of Hardy and Littlewood concerning Fourier series. 7.7. Notes and remarks -- 8. Some applications of the Henstock-Kurzweil integral to double trigonometric series. 8.1. Regularly convergent double series. 8.2. Double Fourier series. 8.3. Some examples of double Fourier series. 8.4. A Lebesgue integrability theorem for double cosine series. 8.5. A Lebesgue integrability theorem for double sine series. 8.6. A convergence theorem for Henstock-Kurzweil integrals. 8.7. Applications to double Fourier series. 8.8. Another convergence theorem for Henstock-Kurzweil integrals. 8.9. A two-dimensional analogue of Boas' theorem. 8.10. A convergence theorem for double sine series. 8.11. Some open problems. 8.12. Notes and remarks. The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus. Henstock-Kurzweil integral. http://id.loc.gov/authorities/subjects/sh86004388 Lebesgue integral. http://id.loc.gov/authorities/subjects/sh94008345 Calculus, Integral. http://id.loc.gov/authorities/subjects/sh85018804 Intégrale de Kurzweil-Henstock. Intégrale de Lebesgue. Calcul intégral. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Calculus, Integral fast Henstock-Kurzweil integral fast Lebesgue integral fast has work: Henstock-Kurzweil integration on Euclidean spaces (Work) https://id.oclc.org/worldcat/entity/E39PCFC3KV6677B4fWg9M6vyh3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Lee, Tuo Yeong, 1967- Henstock-Kurzweil integration on Euclidean spaces. Singapore ; Hackensack, N.J. : World Scientific, ©2011 9789814324588 (OCoLC)724966681 Series in real analysis ; v. 12. http://id.loc.gov/authorities/names/n88505405 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=389631 Volltext |
| spellingShingle | Lee, Tuo Yeong, 1967- Henstock-Kurzweil integration on Euclidean spaces / Series in real analysis ; 1. The one-dimensional Henstock-Kurzweil integral. 1.1. Introduction and Cousin's lemma. 1.2. Definition of the Henstock-Kurzweil integral. 1.3. Simple properties. 1.4. Saks-Henstock lemma. 1.5. Notes and remarks -- 2. The multiple Henstock-Kurzweil integral. 2.1. Preliminaries. 2.2. The Henstock-Kurzweil integral. 2.3. Simple properties. 2.4. Saks-Henstock lemma. 2.5. Fubini's theorem. 2.6. Notes and remarks -- 3. Lebesgue integrable functions. 3.1. Introduction. 3.2. Some convergence theorems for Lebesgue integrals. 3.3. [symbol]-measurable sets. 3.4. A characterization of [symbol]-measurable sets. 3.5. [symbol]-measurable functions. 3.6. Vitali covering theorem. 3.7. Further properties of Lebesgue integrable functions. 3.8. The L[symbol] spaces. 3.9. Lebesgue's criterion for Riemann integrability. 3.10. Some characterizations of Lebesgue integrable functions. 3.11. Some results concerning one-dimensional Lebesgue integral. 3.12. Notes and remarks -- 4. Further properties of Henstock-Kurzweil integrable functions. 4.1. A necessary condition for Henstock-Kurzweil integrability. 4.2. A result of Kurzweil and Jarnik. 4.3. Some necessary and sufficient conditions for Henstock-Kurzweil integrability. 4.4. Harnack extension for one-dimensional Henstock-Kurzweil integrals. 4.5. Other results concerning one-dimensional Henstock-Kurzweil integral. 4.6. Notes and remarks -- 5. The Henstock variational measure. 5.1. Lebesgue outer measure. 5.2. Basic properties of the Henstock variational measure. 5.3. Another characterization of Lebesgue integrable functions. 5.4. A result of Kurzweil and Jarnik revisited. 5.5. A measure-theoretic characterization of the Henstock-Kurzweil integral. 5.6. Product variational measures. 5.7. Notes and remarks. 6. Multipliers for the Henstock-Kurzweil integral. 6.1. One-dimensional integration by parts. 6.2. On functions of bounded variation in the sense of Vitali. 6.3. The m-dimensional Riemann-Stieltjes integral. 6.4. A multiple integration by parts for the Henstock-Kurzweil integral. 6.5. Kurzweil's multiple integration by parts formula for the Henstock-Kurzweil integral. 6.6. Riesz representation theorems. 6.7. Characterization of multipliers for the Henstock-Kurzweil integral. 6.8. A Banach-Steinhaus theorem for the space of Henstock-Kurzweil integrable functions. 6.9. Notes and remarks -- 7. Some selected topics in trigonometric series. 7.1. A generalized Dirichlet test. 7.2. Fourier series. 7.3. Some examples of Fourier series. 7.4. Some Lebesgue integrability theorems for trigonometric series. 7.5. Boas' results. 7.6. On a result of Hardy and Littlewood concerning Fourier series. 7.7. Notes and remarks -- 8. Some applications of the Henstock-Kurzweil integral to double trigonometric series. 8.1. Regularly convergent double series. 8.2. Double Fourier series. 8.3. Some examples of double Fourier series. 8.4. A Lebesgue integrability theorem for double cosine series. 8.5. A Lebesgue integrability theorem for double sine series. 8.6. A convergence theorem for Henstock-Kurzweil integrals. 8.7. Applications to double Fourier series. 8.8. Another convergence theorem for Henstock-Kurzweil integrals. 8.9. A two-dimensional analogue of Boas' theorem. 8.10. A convergence theorem for double sine series. 8.11. Some open problems. 8.12. Notes and remarks. Henstock-Kurzweil integral. http://id.loc.gov/authorities/subjects/sh86004388 Lebesgue integral. http://id.loc.gov/authorities/subjects/sh94008345 Calculus, Integral. http://id.loc.gov/authorities/subjects/sh85018804 Intégrale de Kurzweil-Henstock. Intégrale de Lebesgue. Calcul intégral. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Calculus, Integral fast Henstock-Kurzweil integral fast Lebesgue integral fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh86004388 http://id.loc.gov/authorities/subjects/sh94008345 http://id.loc.gov/authorities/subjects/sh85018804 |
| title | Henstock-Kurzweil integration on Euclidean spaces / |
| title_auth | Henstock-Kurzweil integration on Euclidean spaces / |
| title_exact_search | Henstock-Kurzweil integration on Euclidean spaces / |
| title_full | Henstock-Kurzweil integration on Euclidean spaces / Lee Tuo Yeong. |
| title_fullStr | Henstock-Kurzweil integration on Euclidean spaces / Lee Tuo Yeong. |
| title_full_unstemmed | Henstock-Kurzweil integration on Euclidean spaces / Lee Tuo Yeong. |
| title_short | Henstock-Kurzweil integration on Euclidean spaces / |
| title_sort | henstock kurzweil integration on euclidean spaces |
| topic | Henstock-Kurzweil integral. http://id.loc.gov/authorities/subjects/sh86004388 Lebesgue integral. http://id.loc.gov/authorities/subjects/sh94008345 Calculus, Integral. http://id.loc.gov/authorities/subjects/sh85018804 Intégrale de Kurzweil-Henstock. Intégrale de Lebesgue. Calcul intégral. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Calculus, Integral fast Henstock-Kurzweil integral fast Lebesgue integral fast |
| topic_facet | Henstock-Kurzweil integral. Lebesgue integral. Calculus, Integral. Intégrale de Kurzweil-Henstock. Intégrale de Lebesgue. Calcul intégral. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Calculus, Integral Henstock-Kurzweil integral Lebesgue integral |
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| work_keys_str_mv | AT leetuoyeong henstockkurzweilintegrationoneuclideanspaces |