Definitions of almost periodicity

TL;DR

This paper explores different definitions of almost periodicity for functions on groups with values in uniform spaces, establishing their equivalence to unify the concept across various formulations.

Contribution

It introduces and proves the equivalence of multiple classical definitions of almost periodicity for functions on groups in uniform spaces.

Findings

Various definitions of almost periodicity are shown to be equivalent.

The paper provides a unified framework for understanding almost periodic functions.

It extends classical concepts to functions valued in uniform spaces.

Abstract

Various versions of the classical definitions of (one- and twosided) almost periodicity for functions on groups with values in a uniform space are formulated and their equivalence is shown.