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单词 Sigma Algebra
释义

Sigma Algebra

Let be a Set. Then a -algebra is a nonempty collection of Subsets of such thatthe following hold:

1. The Empty Set is in .

2. If is in , then so is the complement of .

3. If is a Sequence of elements of , then the Union of the s is in .

If is any collection of subsets of , then we can always find a -algebra containing , namely thePower Set of . By taking the Intersection of all -algebras containing , we obtain the smallestsuch -algebra. We call the smallest -algebra containing the -algebra generated by .

See also Borel Sigma Algebra, Borel Space, Measurable Set, Measurable Space,Measure Algebra, Standard Space
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