Given a non-negative measurable function [math]f[/math], we show how to construct a sequence of simple functions monotonically converging to [math]f[/math].
The approximating functions [math]f_n[/math] are defined through a diadic subdivision of the codomain: [math]f_n(x)=\min(n,2^{-n}\cdot floor(2^n f(x)))[/math].
