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Mat. Sb., 2013, Volume 204, Number 8, Pages 83–116 (Mi msb8086)  

This article is cited in 1 scientific paper (total in 1 paper)

On the boundary of the group of transformations leaving a measure quasi-invariant

Yu. A. Neretinabc

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

Abstract: Let $A$ be a Lebesgue measure space. We interpret measures on $A\times A\times \mathbb R^\times$ as ‘maps’ from $A$ to $A$, which ‘spread’ $A$ along itself; their Radon-Nikodym derivatives are also spread. We discuss the basic properties of the semigroup of such maps and the action of this semigroup on the spaces $L^p(A)$.
Bibliography: 26 titles.

Keywords: Lebesgue space, Markov operator, polymorphism, characteristic function, spaces $L^p$.

Funding Agency Grant Number
Austrian Science Fund P22122
State Atomic Energy Corporation ROSATOM H.4e.45.90.11.1059


DOI: https://doi.org/10.4213/sm8086

Full text: PDF file (798 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2013, 204:8, 1161–1194

Bibliographic databases:

UDC: 517.518.112+512.583+517.983.23
MSC: Primary 22F10, 28A35; Secondary 28A33
Received: 17.11.2011 and 04.02.2013

Citation: Yu. A. Neretin, “On the boundary of the group of transformations leaving a measure quasi-invariant”, Mat. Sb., 204:8 (2013), 83–116; Sb. Math., 204:8 (2013), 1161–1194

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. A. Neretin, “Bi-invariant functions on the group of transformations leaving a measure quasi-invariant”, Sb. Math., 205:9 (2014), 1357–1372  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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