# Measurable space

From Encyclopedia of Mathematics

A set with a distinguished ring or -ring (in particular, an algebra or a -algebra) of subsets of .

Examples: with the ring of Jordan-measurable sets (see Jordan measure); with the -ring of sets of finite Lebesgue measure; a topological space with the -algebra of Borel sets (cf. Borel set).

#### References

[1] | P.R. Halmos, "Measure theory" , v. Nostrand (1950) |

**How to Cite This Entry:**

Measurable space.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Measurable_space&oldid=13701

This article was adapted from an original article by V.V. Sazonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article