Multifractal variation measures and multifractal density theorems.

Abstract

In this paper we show that the multifractal Hausdorff measure and multifractal packing measure introduced by Olsen and Peyriere can be expressed as Henstock-Thomson \lq\lq variation" measures. As an application we prove a density theorem for these two measures that extends results by Edgar and is more refined than those found in [Ol1].