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
Famous quotes containing the words formal and/or definition:
“Good gentlemen, look fresh and merrily.
Let not our looks put on our purposes,
But bear it as our Roman actors do,
With untired spirits and formal constancy.”
—William Shakespeare (1564–1616)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
Related Phrases
Related Words