On Vitali-Hahn-Saks-Nikodym type theorems

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 ...

On Hahn-banach Type Theorems for Hilbert C*-modules

We show three Hahn-Banach type extension criteria for (sets of) bounded C*-linear maps of Hilbert C*-modules to the underlying C*-algebras of coefficients. One criterion establishes an alternative description of the property of C*-algebras to be monotone complete or additively complete.

Hahn - Banach theorems

The first point here is that convex sets can be separated by linear functionals. Second, continuous linear functionals on subspaces of a locally convex topological vectorspace have continuous extensions to the whole space. Proofs are for real vectorspaces. The complex versions are corollaries. A crucial corollary is that on locally convex topological vectorspaces continuous linear functionals s...