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Abstract
The Cantor function C [2; p. 213], which appears in analysis as a simple example of a continuous increasing function which is not absolutely continuous, has the following properties:(i)C is defined on [0,1], with C(0) = 0, C (l) = l;(ii)C is continuous and non-decreasing on [0,1];(iii)C is constant on each interval contiguous to the perfect Cantor set P;(iv)C fails to be constant on any open interval containing points of P;(v)The set of points at which C is non-differentiable is non-denumerable.
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