Geodesic
On the boundary of the group of transformations leaving a~measure quasi-invariant
Sbornik. Mathematics, Tome 204 (2013) no. 8, pp. 1161-1194

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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: Markov operator, characteristic function
Mots-clés : Lebesgue space, polymorphism, spaces $L^p$. 
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     author = {Yu. A. Neretin},
     title = {On the boundary of the group of transformations leaving a~measure quasi-invariant},
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     number = {8},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_8_a4/}
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Yu. A. Neretin. On the boundary of the group of transformations leaving a~measure quasi-invariant. Sbornik. Mathematics, Tome 204 (2013) no. 8, pp. 1161-1194. http://geodesic.mathdoc.fr/item/SM_2013_204_8_a4/