The relative multifractal densities: A review and application

Abstract

We are concerned with some density estimations for relative multifractal measures. We tried, through this article, to improve many known density results. The results in this paper establish the connections with various relative multifractal measures and generalize many known results about density theorems. As an application, we mainly discuss the equivalence of the relative multifractal Hausdorff and packing measures on cookie-cutterlike sets satisfying the strong separation condition.

Subject Classification: (2000):

• 28A78
• 28A80

Keywords:

• Multifractal Hausdorff measure
• Multifractal packing measure
• Densities
• Doubling measures
• Cookie-cutter-like sets