Year: 1938
Type: article
Abstract: On continuous functions without a derivative, Fundamenta Mathematicae, vol. 12 (1928), pp.244-253.§ Saks, On the functions of Besicovitch in the space of continuous functions, Fundamenta Mathematicae, vol.19 (1932), pp.211-219.|| It may be recalled that Banach, Über die Baire'sche Kategorie gewisser Funktionenmengen, Studîa Mathematica, vol. 3 (1931), p. 174, has shown that in C the set of functions having at no point a. finite unilateral derivative is of second category.* This is an almost immediate consequence of the existence of non-dense closed sets of positive measure.t The meanings of K(fl), H(fl), and an interval of a set are explained in §2.
Author: Anthony P. Morse
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2090854708