Fatou's Lemma states that for a sequence of non-negative measurable functions, the integral of the limit inferior of the sequence is at most the limit inferior of the integrals of the sequence. Named for Pierre Fatou, it is a basic tool of measure theory used to prove the Dominated and Monotone Convergence Theorems and to justify passing a limit inside an integral.
Facts
StatementFor a sequence of non-negative measurable functions f1, f2, f3 and so on, the Lebesgue integral of the pointwise limit inferior of the sequence is at most the limit inferior of the Lebesgue integrals of the functions in the sequence. 2 Classification
Statement Form Connections
Sources
1. Wikipedia: Fatou's lemma
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In mathematics, Fatou's lemma establishes an inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions.
2. Fatou's Lemma (Wikipedia)
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In mathematics, Fatou's lemma establishes an inequality relating the Lebesgue integral 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.
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