Measurable function: Difference between revisions

Revision as of 21:31, 14 November 2020

Let $(X,M)$ and $(Y,N)$ be measure spaces. A map $f:X\to Y$ is $(M,N)$ -measurable if $f^{-1}(E)\in M$ for all $E\in N.$

A function $f:\mathbb {R} \to {\overline {\mathbb {R} }}$ is called a Lebesgue measurable function if $f$ is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (L, B_{\overline\mathbb{R}}}} - measurable.

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 Let <math>(X,M)</math> and <math>(Y,N)</math> be measure spaces. A map <math>f:X \to Y</math> is '''<math>(M,N)</math>-measurable''' if <math>f^{-1}(E) \in M</math> for all <math>E \in N.</math>
-==Examples of measurable function==
+==Examples of measurable functions==
-*
+* A function <math>f: \mathbb{R} \to \overline{\mathbb{R}}</math> is called a '''Lebesgue measurable function''' if <math>f</math> is <math>(L, B_{\overline\mathbb{R}}}</math>- measurable.