The Vitali-Hahn-Saks Theorem and Measuroids

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 ...

Vitali Coverings and Lebesgue’s Differentiation Theorem

The standard techniques used to prove the Lebesgue differentiation theorem (that monotonic functions are a.e. differentiable) are presented in an unusual way that reveals more about their nature and allows greater generality.