Difference between revisions of "Sigma-algebra"
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That is it is closed under [[Complement|complement]] and [[Countable|countable]] [[Union|union]] | That is it is closed under [[Complement|complement]] and [[Countable|countable]] [[Union|union]] | ||
| + | ==See also== | ||
| + | * [[Types of set algebras]] | ||
| + | ==References== | ||
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{{Definition|Measure Theory}} | {{Definition|Measure Theory}} | ||
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Revision as of 12:39, 14 June 2015
A Sigma-algebra of sets, or σ-algebra is very similar to a σ-ring of sets.
Like how ring of sets and algebra of sets differ, the same applies to σ-ring compared to σ-algebra
Definition
A non empty class of sets S is a σ-algebra if[1]
- if A∈Sthen Ac∈S
- if {An}∞n=1⊂Sthen ∪∞n=1An∈S
That is it is closed under complement and countable union
See also
References
- Jump up ↑ Halmos - Measure Theory - page 28 - Springer - Graduate Texts in Mathematics - 18
