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 ℝⁿ.

中文翻译：

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相对多重分形分析：盒维数、密度和投影

摘要

我们对投影到低维线性子空间下的相对多重分形盒维数、密度结果和多重分形维数的行为感兴趣。本文的结果建立了与各种多重分形和分形维数及其投影的联系，并概括了许多关于 Hausdorff 的已知结果以及 ℝ ⁿ子集的打包度量和维数。