Combinatorics on σ-algebras and problem of Banach

Andrzej Pelc

Displaying similar documents to “Combinatorics on σ-algebras and problem of Banach”

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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. ...

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We show that for a wide class of σ-algebras 𝓐, indicatrices of 𝓐-measurable functions admit the same characterization as indicatrices of Lebesgue-measurable functions. In particular, this applies to functions measurable in the sense of Marczewski.