Order-theoretic properties of some sets of quasi-measures
Zbigniew Lipecki (2017)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
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 show that is order bounded if and only if it is contained in a principal ideal in if and only if it is weakly compact and is contained in a principal ideal in . We also establish some criteria for the coincidence of the ideals, in , generated by and .