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Measurable space

From Encyclopedia of Mathematics
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$ \newcommand{\R}{\mathbb R} \newcommand{\Om}{\Omega} \newcommand{\A}{\mathcal A} \newcommand{\P}{\mathbf P} $

A set with a distinguished σ-algebra of subsets (called measurable). More formally: a pair $(X,\A)$ consisting of a set $X$ and a σ-algebra $\A$ of subsets of $X$.

Examples: $\R^n$ with the Borel σ-algebra; $\R^n$ with the Lebesgue σ-algebra.

References

[1] Terence Tao, "An introduction to measure theory", AMS (2011)
How to Cite This Entry:
Measurable space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Measurable_space&oldid=19853
This article was adapted from an original article by V.V. Sazonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article