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

Let Gms be the group of transformations of a Lebesgue space leaving the measure quasi-invariant. Let Ams be a subgroup of it consisting of transformations preserving the measure. We describe canonical forms of double cosets of Gms by the subgroup Ams and show that all continuous Ams-bi-invariant functions on Gms are functionals of the distribution of a Radon-Nikodym derivative. Bibliography: 14 titles.
Authors:
 [1]
  1. Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22364896
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 9; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; FUNCTIONALS; GROUP THEORY; INVARIANCE PRINCIPLES; MATHEMATICAL SOLUTIONS; SPACE; TRANSFORMATIONS