Timeline for Hutchinson's formula for asymptotically homogeneous Cantor sets
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2013 at 12:38 | comment | added | R W | You are right - the dimension formula I use also holds just under the assumption $\delta_n\to 0$. | |
| Jan 14, 2013 at 6:28 | comment | added | Tapio Rajala | With your fast convergence of $\delta_n$ the measure $m$ has also the property that $m(B(x,r)) \le cr^s$ for all $x \in \mathbb{R}^2$ (with $s = \log 2/ \log 3$). Therefore by Frostman's lemma $\mathcal{H}^s(C_\delta)>0$. For $\dim_\mathcal{H}(C_\delta) = s$ it is enough to assume $\delta_n \to 0$ and $\delta_n \in [0,2/3)$. No fast convergence is needed for this. | |
| Jan 13, 2013 at 23:08 | vote | accept | Nikita Sidorov | ||
| Jan 13, 2013 at 17:38 | comment | added | Nikita Sidorov | Thanks. Yes, introducing measures looks like a good approach here. | |
| Jan 13, 2013 at 15:33 | history | answered | R W | CC BY-SA 3.0 |