Volterra's function

Volterra in 1881, proved that there exists a function, [math]F(x) [/math]whose derivative exists and is bounded for all [math]x\in [a,b][/math], however, the derivative [math]F'(x)[/math] is not Riemann integrable. Actually the derivative is discontinuous on a dense set with positive outer content. It is a very complex function and it is not easy to make a representation. Here there is an approach.

 

Juan Carlos Ponce Campuzano

 
Material Type
Activity
Tags
function  analysis  volterra  derivative  integral 
Target Group (Age)
13 – 19+
Language
English (Australia)
 
 
GeoGebra version
4.2
Views
2086
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