Dye's theorem in the almost continuous category

del Junco, Andres; Sahin, Ayse A.

Dye's theorem in the almost continuous category

Authors

Description

We prove an almost continuous version of Dye's theorem: any two non-atomic probability measure preserving homeomorphisms of Polish spaces are almost continuously orbit equivalent. More precisely they are orbit equivalent by a map which is defined and continuous on a Polish subset of full measure with an inverse satisfying the same conditions. This result includes all of the recent results on almost continuous orbit equivalence. We also deal with the case of infinite invariant measures.