The set of continuous nowhere differentiable functions

R. Daniel Mauldin

Vol. 83 (1979), No. 1, 199–205

DOI: 10.2140/pjm.1979.83.199

Abstract

Let M be the set of all continuous real-valued functions defined on the interval [0,1] which do not have a finite derivative anywhere. It is shown that M forms a coanalytic, non-Borel, subset in the space of all real-valued continuous functions on [0,1] provided with the uniform norm.

Mathematical Subject Classification 2000

Primary: 46E15

Secondary: 26A27

Milestones

Received: 14 August 1978

Published: 1 July 1979