Definition
- Let (X,S,m) be a measure space. Then m is said to be monocompact, if there exist a monocompact family which m-approximates S. A family K of sets in X is said to m-approximate S, if for every element E in S and every nonnegative number g which is less than mE, we have F in S with m-measure greater or equal g, and element in K which contains F and contained in E.
Remark
- See regularly monocompact (measure) for definition of monocompactness of a family of sets.
Reference
- D. H. Fremlin, Weakly α-favourable measure spaces, Fundamenta Mathematicae 165 (2000) http://matwbn.icm.edu.pl/ksiazki/fm/fm165/fm16515.pdf