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Mat. Sb., 2014, Volume 205, Number 9, Pages 145–160 (Mi msb8339)  

Bi-invariant functions on the group of transformations leaving a measure quasi-invariant

Yu. A. Neretinabc

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
c University of Vienna

Abstract: Let $\mathrm{Gms}$ be the group of transformations of a Lebesgue space leaving the measure quasi-invariant. Let $\mathrm{Ams}$ be a subgroup of it consisting of transformations preserving the measure. We describe canonical forms of double cosets of $\mathrm{Gms}$ by the subgroup $\mathrm{Ams}$ and show that all continuous $\mathrm{Ams}$-bi-invariant functions on $\mathrm{Gms}$ are functionals of the distribution of a Radon-Nikodym derivative.
Bibliography: 14 titles.

Keywords: Lebesgue space, transformations of measure spaces, Polish group, double cosets.

Funding Agency Grant Number
Austrian Science Fund P25142


DOI: https://doi.org/10.4213/sm8339

Full text: PDF file (620 kB)
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English version:
Sbornik: Mathematics, 2014, 205:9, 1357–1372

Bibliographic databases:

UDC: 517.986.6+517.987.1+512.546
MSC: Primary 22E66, 28D99, 22F10; Secondary 28E99
Received: 04.02.2014 and 08.06.2014

Citation: Yu. A. Neretin, “Bi-invariant functions on the group of transformations leaving a measure quasi-invariant”, Mat. Sb., 205:9 (2014), 145–160; Sb. Math., 205:9 (2014), 1357–1372

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