On the Measurability of Functions of Two Variables
Roy O. Davies (1973)
Matematický časopis
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Displaying similar documents to “Measurable solutions of functional equations satisfied almost everywhere.”
On the Measurability of Functions of Two Variables
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For a metrizable space X and a finite measure space (Ω, , µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of -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. ...