Order-theoretic properties and separability of some sets of quasi-measures.

Let M and R be algebras of subsets of a set Ω with M⊂R. Denote by E(μ) the set of all quasi-measure extensions of a given quasi-measure μ on M to R. We present some results on the coincidence of the bands, in R, generated by E(μ) and extr E(μ). Moreover, we show that if μ is atomic, then E(μ) is contained in a principal band in R if and only if it is separable. Another sufficient condition for the separability of E(μ) is also presented. [ABSTRACT FROM AUTHOR]