7.3. Measures

Examples 7.3.7(d): Measurable Sets

Show that the intersection of two measurable sets is measurable.
Suppose A and B are measurable. Then comp(A) and comp(B) are also measurable, and because of the previous exercise the set comp(A) comp(B) is measurable.

But since

comp(A) comp(B) = comp(A B)
the set comp(A B) is measurable. Finally, the complement of that set must be measurable, which is what we wanted to prove.
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