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The weak McShane integral

Mohammed Saadoune; Redouane Sayyad — 2014

Czechoslovak Mathematical Journal

We present a weaker version of the Fremlin generalized McShane integral (1995) for functions defined on a $σ$ -finite outer regular quasi Radon measure space $(S, Σ, 𝒯, μ)$ into a Banach space $X$ and study its relation with the Pettis integral. In accordance with this new method of integration, the resulting integral can be expressed as a limit of McShane sums with respect to the weak topology. It is shown that a function $f$ from $S$ into $X$ is weakly McShane integrable on each measurable subset of $S$ if and only if...

Extraction of a “good” subsequence from a bounded sequence of integrable functions.

Saadoune, Mohammed; Valadier, Michel — 1995

Journal of Convex Analysis

Page 1

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