«Assoluta continuità» e «Quasi sub-additività rispetto a una coppia» in spazi di misura

Abstract

A well-known theorem due to J. C. Burkill and some existence theorems for Cesari's integral obtained in [1] are generalized here in measure spaces.

Moreover, the last result, where is used the concept of quasi sub-additivity with respect to two families$(\mathfrak{D},\mathfrak{D}'),\mathfrak{D}' \subset \mathfrak{D}$, and to the mesh for a set function ψ:I↦ψ(I),I ∈ {I}, introduced in [1], is an extension of a theorem obtained by L. Cesari in [5].