Proposition 7.3.11: Monotone Sequences of Measurable Sets

If { A_n } is a sequence of measurable sets that is decreasing, i.e. A_j A_j+1 for all j, and m(A₁) is finite, then

lim m(A_j) = m(A_j)

If { A_n } is a sequence of measurable sets that is increasing in the sense that A_j+1 A_j for all j, then

lim m(A_j) = m(A_j)

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