Timeline for density of fractal measures
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 26, 2018 at 23:20 | comment | added | fedja | You can find an $s$-dimensional set $E_0$ of infinite $H^s$ measure on $[0,1]$, cannot you? Now just take $E=\cup_{a,b\in \mathbb Q, a<b}T_{a,b}E_0$ where $T_{a,b}$ is a linear map of $[0,1]$ onto $[a,b]$. | |
| May 26, 2018 at 23:15 | comment | added | Guo | @fedja I see. I saw a density theorem in a book of Falconer for $0<\mathcal{H}^s(E)<\infty$. However I did not find any density theorem for the case of infinity. Could you give me a reference, or there is a simple construction? Thanks! | |
| May 26, 2018 at 22:56 | comment | added | fedja | You can have $H^s(E\cap I)=+\infty$ for every open interval $I$. What are you going to do then? | |
| May 26, 2018 at 21:52 | review | First posts | |||
| May 26, 2018 at 21:54 | |||||
| May 26, 2018 at 21:51 | history | asked | Guo | CC BY-SA 4.0 |