Nets and sequences of Riemann and Riemann-type integrable functions with values in a Banach space (Q782791)

The authors discuss several aspects of convergence theorems for nets and sequences of Riemann and Riemann-type integrable functions defined on a closed bounded interval in \({\mathbb R}\) with values in a Banach space. They introduce the notion of Riemann \(\Delta\)-Cauchy net of functions and derive correlations with equi-Riemann integrability. Moreover, they establish equi-integrability of the pointwise closure of different types of equi-integrable collections of functions, and study the relative compactness of equi-integrable collections of functions with respect to various topologies.