On a result of Bruckner relating to directional linear categorical density in Euclidean plane

Abstract

Bruckner proved that with exception of a set of first category, all other points of any second category set having Baire property in the Euclidean plane are points of directional linear categorical density of the set in almost all directions in the sense of category. In this article, we investigate this result of Bruckner in relation to sets not necessarily having Baire property and with respect to a more general definition of directional linear categorical density frammed after the pattern originally introduced by Wilczyński for linear categorical density.