Timeline for Why is the Hausdorff measure of this set zero?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 2, 2021 at 13:44 | comment | added | Pietro Majer | I think one can do the extension as you do for any given $\Omega$ without introducing new zeros. Join the balls with a set of arcs so to form a tree (a Christmas tree indeed). Since this is contractible, we can map $\Omega$ to this tree by a smooth map $h$, that also map each ball in itself homeomorphically. We then compose $h$ with a map like you do, that maps each ball by a similarity to the unit ball, and each arc somewhere in the complement. | |
| Jan 2, 2021 at 12:57 | comment | added | Piotr Hajlasz | @PietroMajer You are right. I actually wanted to have a domain homeomorphic to a ball so the extension, but then I realized that I have to remove something. Perhaps I will modify my answer following your suggestion. | |
| Jan 2, 2021 at 0:07 | comment | added | Pietro Majer | In fact one may take $\Omega$ to be the union of the family of balls, skipping the extension & restriction steps | |
| Jan 1, 2021 at 22:54 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
added 1 character in body
|
| Jan 1, 2021 at 22:29 | vote | accept | Bogdan | ||
| Jan 1, 2021 at 18:58 | history | edited | Piotr Hajlasz | CC BY-SA 4.0 |
added 124 characters in body
|
| Jan 1, 2021 at 18:53 | history | answered | Piotr Hajlasz | CC BY-SA 4.0 |