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 ...

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 notion of Cartesian net is introduced in order to provide an appropriate setting for the notion of double limit for directed functions defined on Cartesian products of spaces. As an application, we obtain extensions ...

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 ...