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

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 $L^p(A)$.

37pp pages, 3 figures, corrected version

References in corpus (1)

• Symmetries of Gaussian measures and operator colligations

Cited by in corpus (1)

• Symmetries of Gaussian measures and operator colligations