- Juan Carlos Ponce Campuzano
Volterra in 1881, proved that there exists a function, whose derivative exists and is bounded for all , however, the derivative 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.
Because the function is very complex to define, it is better to show some parts of it. Clic in the boxes for seeing the first three levels of Volterra's function. Reference: Volterra, V. (1881b). Sui Principii del Calcolo Integrale. Giornale di Mathematiche. Vol. XIX, pp. 333-372. Another reference: http://dx.doi.org/10.1080/17498430.2015.1010771