Unconditional convergence and the Vitali-Hahn-Saks theorem
نویسندگان
چکیده
© Mémoires de la S. M. F., 1972, tous droits réservés. L’accès aux archives de la revue « Mémoires de la S. M. F. » (http:// smf.emath.fr/Publications/Memoires/Presentation.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
منابع مشابه
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 ...
متن کاملLIMIT THEOREMS IN (l)-GROUPS WITH RESPECT TO (D)-CONVERGENCE
Some Schur, Vitali-Hahn-Saks and Nikodým convergence theorems for (l)-group-valued measures are given in the context of (D)-convergence. We consider both the σ-additive and the finitely additive case. Here the notions of strong boundedness, countable additivity and absolute continuity are formulated not necessarily with respect to a same regulator, while the pointwise convergence of the measure...
متن کاملOn finitely additive vector measures.
In this paper we extend the well-known Vitali-Hahn-Saks and Nikodým theorems for measures to finitely additive vector-valued set functions.
متن کاملA FUZZY VERSION OF HAHN-BANACH EXTENSION THEOREM
In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.
متن کامل