Fatou's lemma

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 the sequence of integrals of the functions. It is named after the French mathematician Pierre Fatou (1878 - 1929).

Related Topics:
Inequality - Integral - Lebesgue - Limit inferior - Sequence - Function - Pierre Fatou - 1878 - 1929

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Fatou's lemma states that if f1, f2, ... is a sequence of non-negative (measurable) functions, then

Related Topics:
Non-negative - Measurable

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:int liminf_{n ightarrowinfty} f_n leq liminf_{n ightarrowinfty} int f_n.

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Fatou's lemma is proved using the monotone convergence theorem.

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