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Proposition 7.3.14: Monotone Sequences of Measurable Sets

If { An } is a sequence of measurable sets that is decreasing, i.e. Aj Aj+1 for all j, and m(A1) is finite, then
lim m(Aj) = m(Aj)
If { An } is a sequence of measurable sets that is increasing in the sense that Aj+1 Aj for all j, then
lim m(Aj) = m(Aj)
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