Egorov's theorem

The set of Yegorov, ( by DF Egorov ) is a set of measure theory, which shows the relation between pointwise convergence almost everywhere and almost uniform convergence.

Set

Be the - dimensional complex (or real) space and a defined measure on. If this convergence a sequence of functions of complex (or real) measurable functions whose common domain is a - measurable subset of finite measure, almost everywhere ( pointwise ) converges to a measurable function, then is almost evenly.