*Definition [#rf8ad9b4]
-Let (X,S,m) be a measure space. Then m is said to be weakly monocompact, if there exist a monocompact family K with the following property; for every E in S with nonzero m-measure, there is F in S with nonzero m-measure and element in K which contains F and contained in E.

*Remark [#zb09c21b]
-See [[regularly monocompact (measure)]] for definition of monocompactness of a family of sets.

*Reference [#lcd0c8ff]
-D. H. Fremlin, ''Weakly α-favourable measure spaces'', Fundamenta Mathematicae 165 (2000) http://matwbn.icm.edu.pl/ksiazki/fm/fm165/fm16515.pdf