Displaying similar documents to “Adjoint classes of functions in the H 1 sense”

Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion

Tuo-Yeong Lee (2005)

Mathematica Bohemica

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It is shown that a Banach-valued Henstock-Kurzweil integrable function on an m -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function f [ 0 , 1 ] 2 ⟶ ℝ and a continuous function F [ 0 , 1 ] 2 ⟶ ℝ such that ( ) ∫ 0 x ( ) ∫ 0 y f ( u , v ) d v d u = ( ) ∫ 0 y ( ) ∫ 0 x f ( u , v ) d u d v = F ( x , y ) for all ( x , y ) ∈ [ 0 , 1 ] 2 .

Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions

B. Bongiorno, Luisa Di Piazza, Kazimierz Musiał (2006)

Mathematica Bohemica

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We study the integrability of Banach valued strongly measurable functions defined on [ 0 , 1 ] . In case of functions f given by ∑ n = 1 ∞ x n χ E n , where x n belong to a Banach space and the sets E n are Lebesgue measurable and pairwise disjoint subsets of [ 0 , 1 ] , there are well known characterizations for the Bochner and for the Pettis integrability of f (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.

On McShane-type integrals with respect to some derivation bases

Valentin A. Skvortsov, Piotr Sworowski (2006)

Mathematica Bohemica

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Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in ℝ n is given.