International Journal of Mathematics ( IF 0.604 ) Pub Date : 2020-07-25 , DOI: 10.1142/s0129167x20500688
Najmeddine Attia

We develop, in the context of the boundary of a supercritical Galton–Watson tree, a uniform version of large deviation estimate on homogeneous trees to estimate almost surely and simultaneously the Hausdorff and packing dimensions of the Mandelbrot measure over a suitable set $𝒥$. As an application, we compute, almost surely and simultaneously, the Hausdorff and packing dimensions of a fractal set related to covering number on the Galton–Watson tree.

Hausdorff和Mandelbrot度量值的包装尺寸

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