Mathematica Bohemica, Vol. 144, No. 4, pp. 339-355, 2019
Some remarks on descriptive characterizations of the strong McShane integral
Sokol Bush Kaliaj
Received September 5, 2017. Published online August 9, 2018.
Abstract: We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function $f W \to X$ defined on a non-degenerate closed subinterval $W$ of $\mathbb{R}^m$ in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure $V_{\mathcal{M}} F$ generated by the primitive $F \mathcal{I}_W \to X$ of $f$, where $\mathcal{I}_W$ is the family of all closed non-degenerate subintervals of $W$.
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Affiliations: Sokol Bush Kaliaj, Department of Mathematics, Faculty of Natural Science, Aleksander Xhuvani University, Rruga Rinia, Elbasan, Albania, e-mail: sokolkaliaj@yahoo.com
