Lebesgue Orbit Equivalence of Multidimensional Borel Flows

Abstract

The main result of the paper is classification of free multidimensional Borel flows up to Lebesgue Orbit Equivalence, by which we understand an orbit equivalence that preserves the Lebesgue measure on each orbit. Two non smooth Euclidean flows are shown to be Lebesgue Orbit Equivalence if and only if they admit the same number of invariant ergodic probability measures.

Existence of cocompact cross sections is now properly attributed to Clinton Conley

References in corpus (1)

• L^2-Betti numbers of locally compact groups and their cross section equivalence relations

Cited by in corpus (1)

• Cross sections of Borel flows with restrictions on the distance set