Uniform integrability

The uniform integrability is in mathematics reinforcement of the concept of integration. It is primarily in the probability theory of meaning.

Definition

Be a finite measure. A family of integrable functions is called uniformly integrable if

Applies.

Properties

• Each singleton is uniformly integrable.
• If there is a such that for all, as is uniformly integrable.
• A sequence of measurable functions converges in the middle, ie with respect to the norm to a function, if it converges according to the extent and is uniformly integrable.