Spaces of measurable functions

• Autorzy: Piotr Niemiec
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Measurable function; Absolute retract; Infinite-dimensional manifold; Nonatomic measure; Functor of extension

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 54C35: Function spaces
• 57N20: Topology of infinite-dimensional manifolds
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
• 58D15: Manifolds of mappings

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 7
• Strony: 1304-1316

Daty

wydano

2013-07-01

online

2013-04-26

Twórcy

autor

Piotr Niemiec

• Instytut Matematyki, Wydział Matematyki i Informatyki, Uniwersytet Jagiellonski, Łojasiewicza 6, 30-348, Kraków, Poland

Bibliografia

• [1] Banakh T.O., Topology of spaces of probability measures. I. The functors P τ and \(\hat P\) , Mat. Stud., 1995, 5, 65–87 (in Russian), English translation available at http://arxiv.org/abs/1112.6161
• [2] Banakh T.O., Topology of spaces of probability measures. II. Barycenters of Radon probability measures and the metrization of the functors P τ and \(\hat P\) , Mat. Stud., 1995, 5, 88–106 (in Russian), English translation available at http://arxiv.org/abs/1206.1727
• [3] Banakh T., Bessaga Cz., On linear operators extending [pseudo]metrics, Bull. Polish Acad. Sci. Math., 2000, 48(1), 35–49
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• [5] Banakh T., Zarichnyy I., Topological groups and convex sets homeomorphic to non-separable Hilbert spaces, Cent. Eur. J. Math., 2008, 6(1), 77–86 http://dx.doi.org/10.2478/s11533-008-0005-0[WoS][Crossref]
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• [17] Toruńczyk H., Characterizing Hilbert space topology, Fund. Math., 1981, 111(3), 247–262
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Identyfikatory

DOI

10.2478/s11533-013-0236-6