Measures of non-compactness are most commonly used if M is a normed vector space.

Measures of non-compactness are however useful in the study of infinite-dimensional Banach spaces, for example.

In functional analysis, two measures of non-compactness are commonly used; these associate numbers to sets in such a way that compact sets all get the measure 0, and other sets get measures that are bigger according to "how far" they are removed from compactness.