A measure-theoretic characterization of the Henstock-Kurzweil integral revisited

Tuo-Yeong Lee

Displaying similar documents to “A measure-theoretic characterization of the Henstock-Kurzweil integral revisited”

Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space

Lee Tuo-Yeong (2005)

Czechoslovak Mathematical Journal

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Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil integrals in the Euclidean space.

Some full characterizations of the strong McShane integral

Tuo-Yeong Lee (2004)

Mathematica Bohemica

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Some full characterizations of the strong McShane integral are obtained.

Gauge integrals and series

Charles W. Swartz (2004)

Mathematica Bohemica

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This note contains a simple example which does clearly indicate the differences in the Henstock-Kurzweil, McShane and strong McShane integrals for Banach space valued functions.

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 $\sum_{n = 1}^{\infty} x_{n} χ_{E_{n}}$ , 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.