Approximation of measurable functions with simple functions

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].

 

Sisto Baldo

 
Resource Type
Activity
Tags
functions  integral  measurable  simple 
Target Group (Age)
19+
Language
English (United States)
 
 
GeoGebra version
4.2
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2912
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