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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

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

Related:

FatouLebesgueTheorem, MonotoneConvergenceTheorem, DominatedConvergenceTheorem

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

28A20*no label found*

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## Recent Activity

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

new question: Lorenz system by David Bankom

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new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

new question: Lorenz system by David Bankom

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith