Λ-VARIATION AND BAIRE CATEGORY

Abstract

Continuous functions of bounded $\mathrm{\lambda }$-variation that are differentiable at least at one pointform a dense set of first Baire category in $C\mathrm{\Lambda }BV$, the Banach space of continuous functions of bounded $\mathrm{\lambda }$-variation. An example of a nowhere differentiable continuous function of bounded $\mathrm{\lambda }$-variation is given. Furthermore, $C\mathrm{\Lambda }BV$, as a subset of $C[0,1]$ with the usual sup-norm, is a dense subset of first Baire category.