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On Weak Convergence of Hypermeasures
Author(s) -
Haase Hermann
Publication year - 1984
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19841150105
Subject(s) - hyperspace , mathematics , convergence (economics) , bounded function , weak convergence , weak topology (polar topology) , sequence (biology) , topology (electrical circuits) , limit of a sequence , modes of convergence (annotated index) , pure mathematics , mathematical analysis , combinatorics , general topology , topological space , computer science , topological vector space , extension topology , isolated point , computer security , limit (mathematics) , biology , economics , asset (computer security) , genetics , economic growth
Measures on the hyperspace of the closed sets with the FLACHSMEYER‐FELL topology are completely defined by their capacities. A necessary and sufficient condition is given for the weak convergence of a sequence of positive bounded σ‐additive measures on the hyperspace in terms of their capacities.