The integral as an average on a group of translations in a subinvariant measure space

Abstract

Thesis (Ph.D.)--Boston University.If for each i the sequence of points is a finite group if G1 C Gi+l for all i we call the sequence a monotonic sequence of finite groups. Given a measurable group (X,S,1l) with summable on X and a monotonic sequence of finite groups in X, then as Maker has shown, (1) Limit exists a.e. (almost everywhere) and is denoted by f(x) (2) f(x+an)=f(x) for all n (3) f(x) is summable [TRUNCATED