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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 $L^p$.
DOI:
https://doi.org/10.4213/sm8086
 Full text:
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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
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Linking options:
http://mi.mathnet.ru/eng/msb8086https://doi.org/10.4213/sm8086 http://mi.mathnet.ru/eng/msb/v204/i8/p83
Citing articles on Google Scholar:
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This publication is cited in the following articles:
-
Yu. A. Neretin, “Bi-invariant functions on the group of transformations leaving a measure quasi-invariant”, Sb. Math., 205:9 (2014), 1357–1372
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