# Approximation of measurable functions with simple functions

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

Resource Type
Activity
Tags
functions  integral  measurable  simple
Target Group (Age)
19+
Language
English (United States)

GeoGebra version
4.2
Views
2912