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2000/2001 Weak Convergence of Bounded, Monotone Set Functions in an Abstract Setting
Bruno Girotto, Silvano Holzer
Real Anal. Exchange 26(1): 157-176 (2000/2001).


We introduce an abstract treatment of the weak convergence for bounded monotone set functions which allows us to obtain some basic results generalizing well known theorems regarding classical weak and vague convergence and weak convergence of masses on normal topological spaces (e.g. Portmanteau type theorems, Direct and Converse Prokhorov type theorems). Moreover, we introduce a suitable topology (called the L\'evy-topology) in order to study the properties of this abstract convergence from a topological point of view.\newline


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Bruno Girotto. Silvano Holzer. "Weak Convergence of Bounded, Monotone Set Functions in an Abstract Setting." Real Anal. Exchange 26 (1) 157 - 176, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 2 January 2009

zbMATH: 1014.28505
MathSciNet: MR1825501

Primary: 28A33 , 60B05 , Primary28A12 , Secondary60B10

Keywords: Choquet integral , L\'evy-topology , Monotone set function , tightness , weak convergence

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 1 • 2000/2001
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