Automorphisms of the Loeb algebra
David Ross (1987)
Fundamenta Mathematicae
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Displaying similar documents to “Transformations of measurable sets by automorphism groups.”
Automorphisms of the Loeb algebra
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On continuity of measurable group representations and homomorphisms
Yulia Kuznetsova (2012)
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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.