The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set
Matthew Foreman, Friedrich Wehrung (1991)
Fundamenta Mathematicae
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Displaying similar documents to “Combinatorics on σ-algebras and problem of Banach”
The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set
On the average of inner and outer measures
D. Fremlin (1991)
Fundamenta Mathematicae
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Concerning the measurable boundaries of a real function
C. Goffman, R. Zink (1960)
Fundamenta Mathematicae
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Spaces of measurable functions
Piotr Niemiec (2013)
Open Mathematics
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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. ...
Some combinatorial problems on the measurability of functions with respect to invariant extensions of the Lebesgue measure
A. B. Kharazishvili (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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On measurability of vector-valued functions with respect to operators-valued measures
Soledad Rodriguez Salazar (1986)
Extracta Mathematicae
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Some Remarks on Indicatrices of Measurable Functions
Marcin Kysiak (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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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.