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{\bf Question}

Let ${\cal A}$ be a collection of sets.  Can we find a smallest
(in some sense) $\sigma$-algebra containing ${\cal A}$?


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{\bf Answer}

Let $\ds {\cal M}_0=\bigcap_{{\cal M}\supseteq {\cal A}}{\cal M}$
of the collection of all $\sigma$-algebras containing ${\cal A}$
is a $\sigma$-algebra containing ${\cal A}$ and is the smallest.


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