Open Access
2013/2014 Some New Types of Filter Limit Theorems for Topological Group-Valued Measures
Antonio Boccuto, Xenofon Dimitriou
Real Anal. Exchange 39(1): 139-174 (2013/2014).


Some new types of limit theorems for topological group-valued measures are proved in the context of filter convergence for suitable classes of filters. We investigate \((s)\)-boundedness, \(\sigma\)-additivity and regularity properties of topological group-valued measures. We consider also Schur-type theorems, using the sliding hump technique, and prove some convergence theorems in the particular case of positive measures. We deal with the notion of uniform filter exhaustiveness, by means of which we prove some theorems on existence of the limit measure, some other kinds of limit theorems and their equivalence, using known results on existence of countably additive restrictions of strongly bounded measures. Furthermore we pose some open problems.


Download Citation

Antonio Boccuto. Xenofon Dimitriou. "Some New Types of Filter Limit Theorems for Topological Group-Valued Measures." Real Anal. Exchange 39 (1) 139 - 174, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 1 July 2014

zbMATH: 1303.28007
MathSciNet: MR3261904

Primary: 28A33 , 28B10 , 40A35 , 54A20 , 54H11
Secondary: 06E15 , 22A05 , 22A10 , 28A12 , 28B15 , 28C15 , 40C05 , ‎40G15‎ , 41A35 , 41A36 , 54E15

Keywords: (free) filter , (uniform) \(\sigma\)-additivity , (uniform) continuity , (uniform) regularity , (uniform) S boundedness , block-respecting filter , Brooks-Jewett theorem , diagonal filter , Dieudonne theorem , equivalence between limit theorems , filter convergence , Frechet-Nikod\'ym topology , Nikodym convergence theorem , P-filter , sliding hump , Topological Group , uniform filter exhaustiveness , Vitali-Hahn-Saks theorem

Rights: Copyright © 2013 Michigan State University Press

Vol.39 • No. 1 • 2013/2014
Back to Top