English

Abstract

We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function $f\colon W \to X$ 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 $F\colon \mathcal {I}_{W} \to X$ of $f$, where $\mathcal {I}_{W}$ is the family of all closed non-degenerate subintervals of $W$.