Comparing weighted densities

Abstract

Abstract In this paper we study inequalities between weighted densities of sets of natural numbers corresponding to different weight functions. Depending on the asymptotic relation between the weight functions, we give sharp bounds for possible values of one density when the values of another density are given. In particular, we give a condition for two weight functions to generate equivalent weighted densities.

Keywords

• Asymptotic density
• Logarithmic density
• Weighted density