Integration of vector-valued functions with respect to vector measures defined on $δ$-rings

Abstract

This paper extends the theory of scalar-valued integrable functions with respect to vector measures defined on $δ$-rings to the case of vector-valued tensor integrable functions with respect to vector measures defined on $δ$-rings. This paper also generalizes some results of G. F. Stefánsson for tensor integration theory of vector-valued functions with respect to vector measures defined on $σ$-algebras.