A relative multifractal analysis: box-dimensions, densities, and projections

Abstract

We are interested in the behavior of relative multifractal box-dimensions, density results and multifractal dimensions under projections onto a lower-dimensional linear subspace. The results in this paper establish the connections with various multifractal and fractal dimensions and their projections, and generalize many known results about Hausdorff and packing measures and dimensions of a subset of ℝ ⁿ .