Fatou's lemma

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Fatou’s lemma

If $f_{1},f_{2},\dots$ is a sequence of nonnegative measurable functions in a measure space $X$ , then

\int_{X}\liminf_{{n\rightarrow\infty}}f_{n}\leq\liminf_{{n\rightarrow\infty}}% \int_{X}f_{n}

Type of Math Object:

Theorem

Major Section:

Reference

Mathematics Subject Classification

28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence

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