Descriptive properties of σ-porous sets.

Abstract

The main aim of this paper is to construct an absolutely continuous function with non-$\sigma$-porous graph. This answers the question posed by Foran, whether there exists a function of bounded variation with non-$\sigma$-porous graph. As a consequence we obtain a positive solution of Goffman’s question, whether there exists a function with non-$\sigma$-porous graph such that its Fourier series converges uniformly.