Timeline for Examples of polar sets
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 15, 2019 at 18:49 | comment | added | Mateusz Kwaśnicki | Whoops, I misread your question! Of course Cantor sets will typically be non-polar, sorry. I suppose your second question made me think that you are asking about non-polar sets, because as explained in Josiah Park's answer, the logarithmic potential of the 1-D Lebesgue measure on $E \subset \mathbb{R} \times \{0\}$ is bounded on $E$, so if $E$ has positive Lebesgue measure, it is non-polar. | |
| Oct 15, 2019 at 18:47 | answer | added | Alexandre Eremenko | timeline score: 2 | |
| Oct 15, 2019 at 16:05 | answer | added | Josiah Park | timeline score: 2 | |
| Oct 15, 2019 at 13:31 | comment | added | Trusio | Thanks. Anyway, can you be more precise or give me some references? Because a Cantor set is not necessarily polar. I tried to estimate the capacity of a general Cantor set using its construction, but in my estimate when I add the condition to be polar, the Lebesgue measure becomes 0. | |
| Oct 15, 2019 at 10:33 | comment | added | Mateusz Kwaśnicki | A Cantor set will do the job. Take a fat one if you like positive $1$-D Lebesgue measure. In general, any set with positive Hausdorff dimension will be non-polar. | |
| Oct 15, 2019 at 10:17 | history | edited | YCor | CC BY-SA 4.0 |
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| Oct 15, 2019 at 10:00 | review | First posts | |||
| Oct 15, 2019 at 10:14 | |||||
| Oct 15, 2019 at 9:56 | history | asked | Trusio | CC BY-SA 4.0 |