Geodesic
Bi-invariant functions on the group of transformations leaving a~measure quasi-invariant
Sbornik. Mathematics, Tome 205 (2014) no. 9, pp. 1357-1372

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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: transformations of measure spaces, Polish group, double cosets.
Mots-clés : Lebesgue space 
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     author = {Yu. A. Neretin},
     title = {Bi-invariant functions on the group of transformations leaving a~measure quasi-invariant},
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     number = {9},
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     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_9_a5/}
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Yu. A. Neretin. Bi-invariant functions on the group of transformations leaving a~measure quasi-invariant. Sbornik. Mathematics, Tome 205 (2014) no. 9, pp. 1357-1372. http://geodesic.mathdoc.fr/item/SM_2014_205_9_a5/