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

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

2011-11-11

arxiv.org/abs/1111.2833v1

Mathematics

Functional Analysis

29 pages, 3 figures

Scientific paper

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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