Yury A. Neretin
On the Boundary of the Group of Transformations Leaving a Measure Quasi-Invariant
Preprint series: ESI preprints

MSC:

28A33 Spaces of measures, convergence of measures, See Also {46E27, 60Bxx}

28A99 None of the above but in this section

22E65 Infinite-dimensional Lie groups and their Lie algebras, See also {17B65, 58B25, 58H05}

60B15 Probability measures on groups, Fourier transforms, factorization

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 $L^p(A)$.


Keywords: Lebesgue measure space, measurable partition, polymorphism, space $L^p$, measure preserving maps, null-preserving maps, Markov operators, characteristic functions, infinite-dimensional groups