Timeline for Extending the product measure on $2^\omega$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2022 at 7:49 | answer | added | Elliot Glazer | timeline score: 2 | |
| Sep 12, 2017 at 16:57 | answer | added | Alexander Pruss | timeline score: 4 | |
| Sep 11, 2017 at 16:54 | history | edited | Alexander Pruss | CC BY-SA 3.0 |
removed duplication
|
| Sep 11, 2017 at 16:18 | history | edited | Alexander Pruss | CC BY-SA 3.0 |
cleaned up
|
| Sep 11, 2017 at 16:16 | comment | added | Alexander Pruss | Sorry, I had forgotten how the construction went (I came up with it a couple of years ago). I now edited to include the correct construction, but yours is neater and more illuminating, I think. | |
| Sep 11, 2017 at 16:12 | history | edited | Alexander Pruss | CC BY-SA 3.0 |
fixed bad construction
|
| Sep 11, 2017 at 16:00 | comment | added | Alex Kruckman | But I think you can still get a nonmeasurable subset of $\Omega$ with property $H$ by fixing a non-measurable subset $X\subseteq \{0,1\}^{\omega_+}$ and letting $A = \{0\eta\mid \eta\in X\}\cup \{1\eta\mid \eta\notin X\}$. | |
| Sep 11, 2017 at 15:59 | comment | added | Alex Kruckman | Are you sure about your construction of a non-measurable set $A$ with property $H$? $A$ contains exactly one binary sequence with a finite even number of $1$s and exactly one binary sequence with a finite odd number of $1$s (call this number $j$). Then for any $n$, $\rho_n(A)$ contains exactly one binary sequence with a finite even number of $1$s, and that number is either $j+1$ or $j-1$. So $A\cup \rho_n(A)$ contains at most $2$ sequences with a finite even number of $1$s, and the union can't be all of $\Omega$. | |
| Sep 11, 2017 at 14:57 | history | asked | Alexander Pruss | CC BY-SA 3.0 |