Measure-valued almost periodic functions and almost periodic selections of multivalued maps

This article contains a study of Stepanov almost periodic selections of multivalued maps t --> supp mu[.; t], t is an element of R. It is assumed that for a.e. t is an element of R the measure mu[.; t] is a Radon probability measure on a complete metric space and t --> supp mu[.; t], t is an element of R, is a measure-valued almost periodic function.