Displaying similar documents to “The theory of ε -generators and some questions in analysis.”

Spaces of measurable functions

Piotr Niemiec (2013)

Open Mathematics

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For a metrizable space X and a finite measure space (Ω, 𝔐 , µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of 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. ...