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The Egoroff Theorem for Operator-Valued Measures in Locally Convex Spaces

Commun. Math. Anal.
Volume 18, Number 2 (2015), 106 - 111

The Egoroff Theorem for Operator-Valued Measures in Locally Convex Spaces

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Abstract

The Egoroff theorem for measurable ${\mathbb X}$-valued functions and operator-valued measures ${\mathbb m}: \Sigma \to L({\mathbb X}, {\mathbb Y})$ is proved, where $\Sigma$ is a $\sigma$-algebra of subsets of $T \neq \emptyset$ and ${\mathbb X}$, ${\mathbb Y}$ are both locally convex spaces.