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glacier302
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Homework Statement
Let An, n = 1,2,..., be a sequence of measurable sets. Let E = {x: x∈An i.o.}.
(a) Prove that E is a measurable set.
(b) Prove that m(E) = 0 if ∑m(An) < ∞
Homework Equations
A point x is said to be in An infinitely often (i.o.) if there is an infinite sequence of integers n1<n2<... such that x∈Ank for every k.
The Attempt at a Solution
I'm really not sure where to start with part (a). For part (b), if ∑m(An) < ∞
then E is countable, therefore m(E) = 0...I can't really explain why E is countable, though, it's just an instinct.
Any hints would be greatly appreciated : )