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Properties of Measurable Spaces

Let (O,A) be a measurable space.
What do these properties mean?

1) lim sup_n A_n := /_n /_m=n A_n in A
2) lim inf_n A_n := /_n /+m=n A_n in A

keywords: limit, supremum, limsup, liminf

Solution Preview

Ok, these equations define the limsup and liminf of a family of sets
indexed by integers (a sequence of sets). These are supposed to be from A
(to make sense of the statement that limsup and liminf are in A as well).
Please add such assumptions..

Limsup_n A_n = /_n /_{m >= n} A_m (note the index m!)
is the set of all x such that there are infinitely many n such ...

Solution Summary

Measurable spaces are investigated. The solution is detailed and well presented.