Timeline for Binarily universal members of $[0,1]$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2018 at 9:00 | vote | accept | Dominic van der Zypen | ||
| Mar 13, 2018 at 8:56 | answer | added | Bjørn Kjos-Hanssen | timeline score: 3 | |
| Mar 13, 2018 at 8:48 | comment | added | Mateusz Kwaśnicki | For a finite binary string $b$, the set $A_b$ of those $r \in [0, 1]$ which do not contain $b$ as a substring in the binary representation of $b$ is clearly Borel. There are countably many strings $b$, so the union of $A_b$ is also Borel. The set $U$ is the complement of this union. The Lebesgue measure of $A_b$ is zero, so $U$ is of full Lebesgue measure. (Actually, $U$ contains the set of normal numbers, which is of full Lebesgue measure). Does this answer your question? | |
| Mar 13, 2018 at 8:38 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |