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Spaces of measurable functions

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Niemiec P.

Open Mathematics

2013

tom 11

nr 7

1304-1316

For a metrizable space X and a finite measure space (Ω, $\mathfrak{M}$, µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of $\mathfrak{M}$-measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point.

Ograniczanie wyników

1 Open Mathematics

1 Niemiec P.

1 2013

Wyniki wyszukiwania

Spaces of measurable functions