Autore	Muldowney P (Patrick), <1946->
Pubbl/distr/stampa	Hoboken, New Jersey : , : Wiley, , [2021]
Descrizione fisica	1 online resource (382 pages)
Disciplina	519.22
Soggetto topico	Stochastic analysis Henstock-Kurzweil integral Feynman integrals
Soggetto genere / forma	Electronic books.
ISBN	1-119-59552-5 1-119-59550-9 1-119-59554-1
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Record Nr.	UNINA-9910555288603321

Autore	Ostaszewski Krzysztof <1957->
Pubbl/distr/stampa	Providence, Rhode Island : , : American Mathematical Society, , 1986
Descrizione fisica	1 online resource (118 p.)
Disciplina	515.8/3
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Henstock-Kurzweil integral
Soggetto genere / forma	Electronic books.
ISBN	1-4704-0769-8
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	""Table of Contents""; ""Introduction""; ""Chapter 1: Henstock integral""; ""Derivation bases""; ""Derivatives""; ""Henstock integral""; ""Variation""; ""Variational integral""; ""Various ways to define the Henstock integral""; ""Additive bases""; ""Chapter 2: Derivation bases on the plane""; ""Perron integral""; ""Specific bases on the plane""; ""Basic properties of the bases defined""; ""Absolute integration""; ""Lebesgue integral""; ""Comparison of nonabsolute integrals""; ""Differentiation of integrals""; ""Continuity of interval functions""; ""Chapter 3: Generalized Fubini Theorem"" ""Product bases""""Fubini Theorem""; ""Corollaries to the Fubini Theorem""; ""Tolstov's counterexample""; ""Chapter 4: The integral of Kempisty""; ""Functions absolutely continuous in the sense of Kempisty""; ""Burkill integral""; ""Properties of derivatives and the Burkill integral""; ""Semi-absolutely-continuous functions""; ""The relationship between the Kempisty integral and the Î?[sub(2)]-integral""; ""Lebesgue integrability on a nontrivial subinterval""; ""The integrals of Mawhin and Pfeffer""; ""Chapter 5: Approximate derivation bases""; ""Density topologies on the plane"" ""Filtered bases""""Approximate bases""; ""The integral of Chelidze and Dzhvarsheishvili""; ""The relationship of the CD-integral to the other integrals""; ""Bibliography""
Record Nr.	UNINA-9910480685103321

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

Autore	Swartz Charles <1938->
Pubbl/distr/stampa	Singapore ; ; River Edge, N.J., : World Scientific, c2001
Descrizione fisica	1 online resource (150p.)
Disciplina	515/.43
Soggetto topico	Henstock-Kurzweil integral Calculus
Soggetto genere / forma	Electronic books.
ISBN	1-281-95631-7 9786611956318 981-281-065-X
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Introduction to the gauge or Henstock-Kurzweil integral; basic properties of the gauge integral; Henstock's Lemma and improper integrals; the gauge integral over unbounded intervals; convergence theorems; integration over more general sets -Lebesgue measure; the space of gauge integrable functions; multiple integrals and Fubini's theorem; the McShane integral; McShane integrability is equivalent to absolute Henstock-Kurzweil integrability.
Record Nr.	UNINA-9910453187603321

Autore	Briend Jean-Yves
Pubbl/distr/stampa	Les Ulis : , : ECP sciences, , [2014]
Descrizione fisica	1 online resource (300 p.)
Collana	Collection Grenoble sciences
Soggetto topico	Integration, Functional Riemann integral Henstock-Kurzweil integral
Soggetto genere / forma	Electronic books.
ISBN	2-7598-1691-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	fre
Nota di contenuto	Front matter -- Avant-propos -- Table des matières -- Introduction -- Partie I – Intégration des fonctions d’une variable réelle -- Chapitre 1 – Quelques rappels d’analyse -- Chapitre 2 – Des aires aux primitives, et vice versa -- Chapitre 3 – Fonctions intégrables, intégrale -- Chapitre 4 – Propriétés élémentaires de l’intégrale -- Chapitre 5 – Intégrales et primitives -- Chapitre 6 – Intégrales impropres -- Partie II – Intégrale de Lebesgue, théorèmes de convergence et séries de Fourier -- Chapitre 7 – Ensembles de mesure nulle et notion de « presque partout » -- Chapitre 8 – Les théorèmes de convergence. Applications -- Chapitre 9 – Séries de Fourier -- Partie III – Intégration des fonctions de plusieurs variables réelles et espaces de Lebesgue -- Chapitre 10 – Intégration des fonctions de plusieurs variables -- Chapitre 11 – Mesure de Lebesgue, espaces Lp, applications -- Partie IV – Exercices, fascicule de résultats -- Chapitre 12 – Exercices -- Chapitre 13 – Fascicule de résultats -- Bibliographie -- Index
Record Nr.	UNINA-9910460034703321