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Let be a Set. Then a
-algebra
is a nonempty collection of Subsets of
such that
the following hold:
If is any collection of subsets of
, then we can always find a
-algebra containing
, namely the
Power Set of
. By taking the Intersection of all
-algebras containing
, we obtain the smallest
such
-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