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Record Nr. |
UNINA9910788961403321 |
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Autore |
Lee Tuo Yeong <1967-> |
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Titolo |
Henstock-Kurzweil integration on euclidean spaces [[electronic resource] /] / Lee Tuo Yeong |
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Pubbl/distr/stampa |
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Singapore ; ; Hackensack, N.J., : World Scientific, c2011 |
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ISBN |
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1-283-23477-7 |
9786613234773 |
981-4324-59-0 |
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Descrizione fisica |
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1 online resource (325 p.) |
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Collana |
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Series in real analysis ; ; v. 12 |
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Classificazione |
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Disciplina |
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Soggetti |
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Henstock-Kurzweil integral |
Lebesgue integral |
Calculus, Integral |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and indexes. |
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Nota di contenuto |
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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 |
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