Category:Convergence in Measure
Jump to navigation
Jump to search
This category contains results about Convergence in Measure.
Let $\struct {X, \Sigma, \mu}$ be a measure space.
Let $\sequence {f_n}_{n \mathop \in \N}, f_n: X \to \R$ be a sequence of $\Sigma$-measurable functions.
Then $f_n$ is said to converge in measure to a measurable function $f: X \to \R$ if and only if:
- $\ds \forall \epsilon \in \R_{>0}: \lim_{n \mathop \to \infty} \map \mu {\set {x \in D : \size {\map {f_n} x - \map f x} \ge \epsilon} } = 0$
for all $D \in \Sigma$ with $\map \mu D < + \infty$.
Pages in category "Convergence in Measure"
The following 2 pages are in this category, out of 2 total.