In mathematics, Fatou`s lemma establishes an inequality relating the integral (in the sense of Lebesgue) of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma is named after Pierre Fatou. Fatou`s lemma can be used to prove the Fatou–Lebesgue theorem and Lebesgue`s dominated convergen......
Found on
http://en.wikipedia.org/wiki/Fatou`s_lemma
Let {X
n} for n=1,2,3,... be a sequence of nonnegative real random variables. Then lim inf
n->infinity E[X
n] = E[lim inf
n->infinity X
n]. Source: Durrett, 1996, p 16 Contexts: probability
Found on
http://www.econterms.com/glossary.cgi?query=Fatou's+lemma
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