Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The sum of Rademacher functions and Hausdorff dimension

Tian-You Hua1 and Ka-Sing Laua1

a1 Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

Abstract

For 0 < α < 1, let S0305004100068985_inline1 for 0 ≤ x < 1, where S0305004100068985_inline2 is the sequence of Rademacher functions. We give a class of fα so that their graphs have Hausdorff dimension 2 − α. The result is closely related to the corresponding unsolved question for the Weierstrass functions.

(Received August 29 1989)