Compactness in spaces of group-valued contents, the Vitali-Hahn-Saks theorem and Nikodym's boundedness theorem

Unconditional convergence and the Vitali-Hahn-Saks theorem

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The Vitali { Hahn { Saks theorem for theprodu t of quantum logi sAnna

A Survey of the Vitali-hahn-saks Theorem with an Application in Probability Theory

Introduced by Vitali(1907), Hahn(1922) and Saks(1933), the VitaliHahn-Saks theorem plays a vital role in measure theory in proving some weak convergence theorems. In this Toolbox Essay, we will first introduce the Nikodym theorem followed by a self-contained proof. Next, we state the Vitali-Hahn-Saks theorem and show by an example how this theorem can be used in probability theory. The benefit ...

The Vitali covering theorem in constructive mathematics

This paper investigates the Vitali Covering Theorem from various constructive angles. A Vitali Cover of a metric space is a cover such that for every point there exists an arbitrarily small element of the cover containing this point. The Vitali Covering Theorem now states, that for any Vitali Cover one can find a finite family of pairwise disjoint sets in the Vitali Cover that cover the entire ...

The Uniform Boundedness Theorem in Asymmetric Normed Spaces

and Applied Analysis 3 The condition of right K-completeness for X, p leaves outside the scope of this theorem an important class of asymmetric normed spaces, the asymmetric normed spaces associated to normed lattices because these spaces are right K-complete only for the trivial case 13 . In this paper, we give a uniform boundedness type theorem in the setting of asymmetric normed spaces which...