Displaying similar documents to “On LCA groups each of whose characters is ultimately measurable”

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.

A note on intersections of non-Haar null sets

Eva Matoušková, Miroslav Zelený (2003)

Colloquium Mathematicae

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We show that in every Polish, abelian, non-locally compact group G there exist non-Haar null sets A and B such that the set {g ∈ G; (g+A) ∩ B is non-Haar null} is empty. This answers a question posed by Christensen.

On continuity of measurable group representations and homomorphisms

Yulia Kuznetsova (2012)

Studia Mathematica

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Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space ℒ(H) of bounded linear operators on H with the weak operator topology. We prove that if U is a measurable map from G to ℒ(H) then it is continuous. This result was known before for separable H. We also prove that the following statement is consistent with ZFC: every measurable homomorphism from a locally compact group into any topological group is continuous.

On measurable relation

C. Himmelberg, T. Parthasarathy, F. Van Vleck (1981)

Fundamenta Mathematicae

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Measurable cardinals and fundamental groups of compact spaces

Adam Przeździecki (2006)

Fundamenta Mathematicae

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We prove that all groups can be realized as fundamental groups of compact spaces if and only if no measurable cardinals exist. If the cardinality of a group G is nonmeasurable then the compact space K such that G = π₁K may be chosen so that it is path connected.

On the difference property of families of measurable functions

Rafał Filipów (2003)

Colloquium Mathematicae

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We show that, generally, families of measurable functions do not have the difference property under some assumption. We also show that there are natural classes of functions which do not have the difference property in ZFC. This extends the result of Erdős concerning the family of Lebesgue measurable functions.