Outer measure

cosmos 8th October 2017 at 8:21pm

Like a Measure but where additivity is replaced by sub-additivity, that is:

μ(i=1Ei)i=1μ(Ei)\mu(\bigcup\limits_{i=1}^{\infty} E_i) \leq \sum\limits_{i=1}^{\infty} \mu(E_i) for any collection E1,E2,...AE_1, E_2, ... \in \mathcal{A} of mutually disjoint sets.