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Accessible literature on fractional dimensions of subsets of $\mathbb R^n$

The book Fractal Geometry - Mathematical Foundations and Applications by Kenneth Falconer may be what you are looking for. As far as I recall, everything is done in $\mathbb{R}^n$ and he tries to keep ...
anon's user avatar
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4 votes

Accessible literature on fractional dimensions of subsets of $\mathbb R^n$

Erin Pearse's Introduction to dimension theory and fractal geometry may well be suited for this purpose. It introduces the various ways to define and measure a fractional dimension (box counting, ...
Carlo Beenakker's user avatar
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Intersection of IID fractal sets

No. They may be almost surely disjoint. If $y\in\{0,1\}^{\mathbb N}$, let $S_y$ denote the (closure of the) set of $x$'s in $[0,1]$ such that the $2^n$th binary digit of $x$ is $y_n$; and the $(2^n+1)$...
Anthony Quas's user avatar
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