The fractional dimensions of intersections of the Besicovitch sets and the Erdös–Rényi sets

In this paper, we completely determine the Hausdorff dimension and packing dimension of the intersections of two kinds of typical level sets, in which one is the Besicovitch sets and the other is the Erdös–Rényi sets with relation to the well-known Erdös–Rényi limit theorem. Our research extends the work of Besicovitch in another direction and simultaneously complements the Erdös–Rényi limit theorem from the point of view of dimension theory.