Uniform Integrability - Formal Definition

Formal Definition

The following definition applies.

• A class of random variables is called uniformly integrable(UI) if given, there exists such that, where is the indicator function .

• An alternative definition involving two clauses may be presented as follows: A class of random variables is called uniformly integrable if:
  • There exists a finite such that, for every in, .
  • For every there exists such that, for every measurable such that and every in, .