Ramsey properties of finite measure algebras and topological dynamics of the group of measure preserving automorphisms: Some results and an open problem

Abstract

We study in this paper ordered finite measure algebras from the point of view of Fräissé and Ramsey theory. We also propose an open problem, which is a homogeneous version of the Dual Ramsey Theorem of Graham- Rothschild, and derive consequences of a positive answer to the study of the topological dynamics of the automorphism group of a standard probability space and also the group of measure preserving homeomorphisms of the Cantor space.