Second Peano derivatives are not extendable (Q1822647)

It is known that a real function defined and differentiable on a perfect subset of the real line can be extended to be a function defined and differentiable everywhere. The paper shows that in general there is no extension theorem for the second Peano derivative defined on a suitable perfect set. (The first Peano derivatives coincide with the ordinary derivatives.) This answers a question raised by C. E. Weil.