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

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

2011-01-25

arxiv.org/abs/1101.4708v1

Mathematics

Functional Analysis

8 pages

Scientific paper

The Egoroff theorem for measurable $\bold X$-valued functions and
operator-valued measures $\bold m: \Sigma \to L(\bold X, \bold Y)$, where
$\Sigma$ is a $\sigma$-algebra of subsets of $T \neq \emptyset$ and $\bold X$,
$\bold Y$ are both locally convex spaces, is proved. The measure is supposed to
be atomic and the convergence of functions is net.

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