Category:Fatou's Lemma for Measures

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This category contains pages concerning Fatou's Lemma for Measures:

Let $\struct {X, \Sigma, \mu}$ be a measure space.

Let $\sequence {E_n}_{n \mathop \in \N} \in \Sigma$ be a sequence of $\Sigma$-measurable sets.


$\ds \map \mu {\liminf_{n \mathop \to \infty} E_n} \le \liminf_{n \mathop \to \infty} \map \mu {E_n}$


$\ds \liminf_{n \mathop \to \infty} E_n$ is the limit inferior of the $E_n$
the right hand side limit inferior is taken in the extended real numbers $\overline \R$.