×

Stronger estimates of smallness of sets of Fréchet nondifferentiabiliy of convex functions. (English) Zbl 0547.46026

Let f be a continuous function on a real Banach space with a separable dual. According to a well-known result of Asplund, the set \(N_ f\) of points at which f is not Frechet differentiable is meagre. In a preceding article the authors improved this result by showing that \(N_ f\) is even \(\sigma\) -porous. In the present article they give a stronger estimate of the smallness of \(N_ f\) and they show that this estimate is close to a complete characterization. These results are also generalized to obtain stronger estimates of smallness of exceptional sets associated with monotone operators.

MSC:

46G05 Derivatives of functions in infinite-dimensional spaces
46B10 Duality and reflexivity in normed linear and Banach spaces
47H05 Monotone operators and generalizations
PDFBibTeX XMLCite