Sigma-algebra
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A Sigma-algebra of sets, or [ilmath]\sigma[/ilmath]-algebra is very similar to a [ilmath]\sigma[/ilmath]-ring of sets.
Like how ring of sets and algebra of sets differ, the same applies to [ilmath]\sigma[/ilmath]-ring compared to [ilmath]\sigma[/ilmath]-algebra
Definition
A non empty class of sets [ilmath]S[/ilmath] is a [ilmath]\sigma[/ilmath]-algebra if[1]
- if [math]A\in S[/math] then [math]A^c\in S[/math]
- if [math]\{A_n\}_{n=1}^\infty\subset S[/math] then [math]\cup^\infty_{n=1}A_n\in S[/math]
That is it is closed under complement and countable union
References
- ↑ Halmos - Measure Theory - page 28 - Springer - Graduate Texts in Mathematics - 18
