Definable subgroups of measure algebras

摘要

We show that type-definable subgroups of measure algebras are definable. This paper deals with type-definable subgroups of an atomless measure algebra associated to a probability space. The model theoretic framework that we will use in this paper is the one of metric structrues as presented in [6,3], In this paper, the notion of definable sets from [6] will play a very important role. the backgroud on measure algebras for this paper comes from [2] and [5].