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Results tagged with dimension-theory
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user 48839
Hausdorff dimension, box dimension, packing dimension and similar concepts.
20
votes
Accepted
A set whose Hausdorff dimension gradually changes?
I assume you want a set $A\subseteq [0,1]$ such that $\dim (A\cap [0,x])=x$ for all $x$. We can define $A_1$ by taking the union of a (Borel) subset of dimension $0$ of $[0,1/2]$ with a subset of dime …
- 24.2k
4
votes
Accepted
Random Cantor sets on the unit interval
Like the classical Cantor set, your set has a natural representation $C=\bigcap C_n$, where $C_1\supseteq C_2\supseteq C_3\supseteq\ldots$, and each $C_n$ is a disjoint union of $2^{n-X_n}$ intervals …
- 24.2k