Category:Fatou's Lemma for Measures
Jump to navigation
Jump to search
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.
Then:
- $\ds \map \mu {\liminf_{n \mathop \to \infty} E_n} \le \liminf_{n \mathop \to \infty} \map \mu {E_n}$
where:
- $\ds \liminf_{n \mathop \to \infty} E_n$ is the limit inferior of the $E_n$
- the right hand side limit inferior is taken in the extended real numbers $\overline \R$.
Pages in category "Fatou's Lemma for Measures"
The following 4 pages are in this category, out of 4 total.