Vol. 83, No. 1, 1979

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The set of continuous nowhere differentiable functions

R. Daniel Mauldin

Vol. 83 (1979), No. 1, 199–205
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
Authors
R. Daniel Mauldin
Department of Mathematics
University of North Texas
Denton TX 76203-1430
United States
www.math.unt.edu/~mauldin