Preiss, D.; Zajíček, L. Stronger estimates of smallness of sets of Fréchet nondifferentiabiliy of convex functions. (English) Zbl 0547.46026 Suppl. Rend. Circ. Mat. Palermo, II. Ser. 3, 219-223 (1984). 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. Cited in 6 Documents MSC: 46G05 Derivatives of functions in infinite-dimensional spaces 46B10 Duality and reflexivity in normed linear and Banach spaces 47H05 Monotone operators and generalizations Keywords:smallness of sets of Frechet nondifferentiability of convex functions; real Banach space with a separable dual; meagre; \(\sigma\) -porous; smallness of exceptional sets associated with monotone operators PDFBibTeX XMLCite \textit{D. Preiss} and \textit{L. Zajíček}, Suppl. Rend. Circ. Mat. Palermo (2) 3, 219--223 (1984; Zbl 0547.46026)