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)