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arXiv · 1111.2833

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

Yury Neretin
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Abstract

Let $A$ be a Lebesgue measure space. We interpret measures on $A\times A\times R_+$ as 'maps' from $A$ to $A$, which spread $A$ along itself; their Radon-Nikodym derivatives also are spread. We discuss basic properties of the semigroup of such maps and the action of this semigroup in the spaces $L^p(A)$.

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Yury Neretin. 2011-11-11. On the boundary of the group of transformations leaving a measure quasi-invariant. https://doi.org/10.4213/sm8086, 10.1070/sm2013v204n08abeh004335

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