Question

State and prove fatou’s lemma.

Answer 1

Fatou's lemma. 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. ... Fatou's lemma can be used to prove the Fatou–Lebesgue theorem and Lebesgue's dominated convergence theorem.

Answer 2

Fatou's lemma , in math establishes the inequality the Lebesgue integral of the limit inferior of the sequence of function to the limit this can be used to proof the same theorem and Lebesgue theorem