Timeline for Density measure on $\mathbb{N}^2$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 5, 2016 at 19:30 | comment | added | Anthony Quas | Alternatively (and probably a bit more naturally), how about $\limsup_{m,n\to\infty}|A\cap [1,\ldots,n]\times [1,\ldots,m]|/mn$? | |
| Sep 5, 2016 at 11:23 | comment | added | Goldstern | Even monotonicity will not give uniqueness. You could define $\mu_2'(U)= \sup_{A\times B\subseteq U} \mu(A)\cdot \mu(B)$. Then the diagonal (or identity function) will have measure $0$, but measure $1$ with my previous definition. | |
| Sep 5, 2016 at 11:14 | vote | accept | Dominic van der Zypen | ||
| Sep 5, 2016 at 10:42 | history | answered | Goldstern | CC BY-SA 3.0 |