Fatou’s lemma

If $f_1,f_2,\mathrm{\dots }$ is a sequence of nonnegative measurable functions in a measure space $X$, then

$${\int }_X\underset{n\to \mathrm{\infty }}{lim\; inf}{f}_n\le \underset{n\to \mathrm{\infty }}{lim\; inf}{\int }_X{f}_n$$

Title	Fatou’s lemma
Canonical name	FatousLemma
Date of creation	2013-03-22 13:12:50
Last modified on	2013-03-22 13:12:50
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	6
Author	Koro (127)
Entry type	Theorem
Classification	msc 28A20
Related topic	FatouLebesgueTheorem
Related topic	MonotoneConvergenceTheorem
Related topic	DominatedConvergenceTheorem