F\(''\)utility on nowhere dense sets (Q1978837)

The author discusses the notion of second derivative of a function \(f\) defined on a closed nowhere dense set \(H\). He is interested in relationships between this notion and approximation by a quadratic polynomial (\(f\) is approximated by a quadratic polynomial at \(x\) if \(\lim _{y\in H,y \to x}(f(y)-f(x)-(y-x)f'(x))/(y-x)^2\) exists), extendibility of \(f\) and convexity of \(f\).