## Proposition 7.3.14: Monotone Sequences of Measurable Sets

If

*{*is a sequence of measurable sets that is decreasing, i.e.**A**_{n}}*for all***A**_{j}**A**_{j+1}*j*, and*m(*) is finite, then**A**_{1}Iflim m(A_{j}) = m(A_{j})

*{*is a sequence of measurable sets that is increasing in the sense that**A**_{n}}*for all***A**_{j+1}**A**_{j}*j*, thenlim m(A_{j}) = m(A_{j})