We give extensions of the Lusin’s Theorem, the Severini-Egorov’s Theorem, and the Riesz Subsequence Theorems to the setting of a non-additive vector valued set functions and sequences of functions taking values in general ...

We use an extended theory of integral that generalizes the integration of vector valued functions with respect to non-negative, monotonic,countably subadditive set functions, in order to introduce a new approach to stochastic ...

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 ...

In this paper, we introduce and study a metric-like (non-necessarily metric) topology that is weaker than the original topology of a given topological space. The results are used to provide more useful and more general ...

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 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 ...

We investigate the common features and the resemblance of the central parts of the different existing integration theories to obtain a more unified approach to the notion of integral. Our approach gives a presentation of ...