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Henstock-Kurzweil integration on euclidean spaces [[electronic resource] /] / Lee Tuo Yeong
| Henstock-Kurzweil integration on euclidean spaces [[electronic resource] /] / Lee Tuo Yeong |
| Autore | Lee Tuo Yeong <1967-> |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2011 |
| Descrizione fisica | 1 online resource (325 p.) |
| Disciplina | 515.43 |
| Collana | Series in real analysis |
| Soggetto topico |
Henstock-Kurzweil integral
Lebesgue integral Calculus, Integral |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-23477-7
9786613234773 981-4324-59-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; 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 μm-measurable sets; 3.4 A characterization of μm-measurable sets
3.5 μm-measurable functions3.6 Vitali Covering Theorem; 3.7 Further properties of Lebesgue integrable functions; 3.8 The Lp 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 Jarn ́ık; 4.3 Some necessary and su cient conditions for Henstock- Kurzweil integrability 4.4 Harnack extension for one-dimensional Henstock-Kurzweil integrals4.5 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 Jarn ́ık 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 parts6.2 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 test7.2 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 |
| Record Nr. | UNINA-9910464534003321 |
Lee Tuo Yeong <1967->
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Henstock-Kurzweil integration on euclidean spaces [[electronic resource] /] / Lee Tuo Yeong
| Henstock-Kurzweil integration on euclidean spaces [[electronic resource] /] / Lee Tuo Yeong |
| Autore | Lee Tuo Yeong <1967-> |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2011 |
| Descrizione fisica | 1 online resource (325 p.) |
| Disciplina | 515.43 |
| Collana | Series in real analysis |
| Soggetto topico |
Henstock-Kurzweil integral
Lebesgue integral Calculus, Integral |
| ISBN |
1-283-23477-7
9786613234773 981-4324-59-0 |
| Classificazione |
SK 430
SK 620 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; 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 μm-measurable sets; 3.4 A characterization of μm-measurable sets
3.5 μm-measurable functions3.6 Vitali Covering Theorem; 3.7 Further properties of Lebesgue integrable functions; 3.8 The Lp 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 Jarn ́ık; 4.3 Some necessary and su cient conditions for Henstock- Kurzweil integrability 4.4 Harnack extension for one-dimensional Henstock-Kurzweil integrals4.5 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 Jarn ́ık 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 parts6.2 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 test7.2 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 |
| Record Nr. | UNINA-9910788961403321 |
|
Lee Tuo Yeong <1967->
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||