Nowhere monotone and Cantor functions (Q1098950)

For f: [a,b]\(\to R\) let \(\alpha [f](t)=\sup f([a,t])\), \(t\in [a,b]\), be called the associate of f. A continuous function \(f: [a,b]\to R\) is called a Cantor function when its set of constancy \(K(f)=\{x\in [a,b]:\) f is constant on some neighborhood of \(x\}\) is a dense, proper subset of \([a,b].\) In this paper the authors investigate some properties differentiability properties) of associates of continuous functions, the class of differentiable Cantor functions and the relationship between Cantor functions and the monotone-light factorization of continuous functions.