Sigma-algebra: Difference between revisions
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A '''<math>\sigma</math>-algebra''' is an [[algebra]] that is closed under countable unions. Thus a <math>\sigma</math>-algebra is a nonempty collection ''A'' of subsets of a nonempty set ''X'' closed under countable unions and complements. | A '''<math>\sigma</math>-algebra''' is an [[algebra]] that is closed under countable unions. Thus a <math>\sigma</math>-algebra is a nonempty collection ''A'' of subsets of a nonempty set ''X'' closed under countable unions and complements. | ||
==Examples of <math>\sigma</math>-algebras== | |||
* Given a set <math>X</math>, then <math>2^X</math> and <math>\{\emptyset,X\}</math> are <math>\sigma</math>-algebras. | |||
Revision as of 06:13, 8 October 2020
This page is under construction.
A -algebra is an algebra that is closed under countable unions. Thus a -algebra is a nonempty collection A of subsets of a nonempty set X closed under countable unions and complements.
Examples of -algebras
- Given a set , then and are -algebras.
