Real Analysis Exchange
- Real Anal. Exchange
- Volume 26, Number 1 (2000), 157-176.
Weak Convergence of Bounded, Monotone Set Functions in an Abstract Setting
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
Real Anal. Exchange, Volume 26, Number 1 (2000), 157-176.
First available in Project Euclid: 2 January 2009
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Girotto, Bruno; Holzer, Silvano. Weak Convergence of Bounded, Monotone Set Functions in an Abstract Setting. Real Anal. Exchange 26 (2000), no. 1, 157--176. https://projecteuclid.org/euclid.rae/1230939151