The Lebesgue-Nikodým Theorem states that for a Lebesgue measure λ:Σ〖⊂2〗^Ω→[0,∞) an additive set function F:Σ→R which is λ-absolutely continuous is the integral of a Lebegsue integrable a measurable function ...

We revisit the definition of the tensor integrability introduced in [1], and prove some useful characterizations that provide a foundation for studying relevant properties to the integration theory. As applications, we ...

We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces ...