Variational Henstock integrability of Banach space valued functions.

Autor: Di Piazza, Luisa
Další autoři:
Jazyk: angličtina
Předmět:
Druh dokumentu: Non-fiction
ISSN: 0862-7959
Abstrakt: Abstract: We study the integrability of Banach space valued strongly measurable functions defined on [0,1]. In the case of functions f given by \sum\nolimits_{n=1}^{\infty} x_n\chi_{E_n}, where x_n are points of a Banach space and the sets E_n are Lebesgue measurable and pairwise disjoint subsets of [0,1], there are well known characterizations for Bochner and Pettis integrability of f. The function f is Bochner integrable if and only if the series \sum\nolimits_{n=1}^{\infty}x_n|E_n| is absolutely convergent. Unconditional convergence of the series is equivalent to Pettis integrability of f. In this paper we give some conditions for variational Henstock integrability of a certain class of such functions.
Databáze: Katalog Knihovny AV ČR