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 convergence theorem.
Read more about Fatou's Lemma: Standard Statement of Fatou's Lemma, Examples For Strict Inequality, A Counterexample, Reverse Fatou Lemma, Fatou's Lemma For Conditional Expectations