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Nonmeasurable automorphisms of Lie groups relative to real- and non-archimedean-valued measures. (English. Russian original) Zbl 1370.22009

J. Math. Sci., New York 185, No. 1, 1-34 (2012); translation from Sovrem. Mat. Prilozh. 73 (2011).
Summary: We study the problem on the existence of nonmeasurable automorphisms of finite-dimensional and infinite-dimensional Lie groups over the field of real numbers and also over non-Archimedean local fields. The nonmeasurability of automorphisms is considered relative to real-valued measures and also measures with values in non-Archimedean local fields. Their existence is proved and a procedure for their construction is given. Their application to the construction of nonmeasurable irreducible unitary representations is demonstrated.

MSC:

22E30 Analysis on real and complex Lie groups
28E05 Nonstandard measure theory
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