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, .
Read more about this topic: Uniform Integrability
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