Order boundedness and weak compactness of the set of quasi-measure extensions of a quasi-measure
Zbigniew Lipecki (2015)
Commentationes Mathematicae Universitatis Carolinae
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Let and be algebras of subsets of a set with , and denote by the set of all quasi-measure extensions of a given quasi-measure on to . We give some criteria for order boundedness of in , in the general case as well as for atomic . Order boundedness implies weak compactness of . We show that the converse implication holds under some assumptions on , and or alone, but not in general.