The irregular Cantor sets Ce ([0, 1]) and Cπ ([0, 1]), and the Cantor- Lebesgue irregular functions Ge and Gπ

Abstract

In this article, we introduce and study a new class of perfect nowhere-dense sets, which are not selfsimilar in any subset, also, we constructed the correspondent singular functions. We construct a twodimensional irregular Cantor set Ce,π ([0, 1]) on the real plane.