Saeki’s improvement of the Vitali-Hahn-Saks-Nikodým theorem holds precisely for Banach spaces having cotype

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 ...

Cotype of Some Banach Spaces

Type and cotype are computed for Banach spaces generated by some positive sublinear operators and Banach function spaces. Applications of the results yield that under certain assumptions Clarkson’s inequalities hold in these spaces.

Hahn-banach Theorem

We prove a version of Hahn-Banach Theorem. and 1] provide the notation and terminology for this paper. The following propositions are true: (1) For all sets x, y and for every function f such that h hx; yi i 2 f holds y 2 rng f: (2) For every set X and for all functions f, g such that X dom f and f g holds fX = gX: (3) For every non empty set A and for every set b such that A 6 = fbg there exis...