Timeline for Measure dependance of groupoid von Neumann algebra
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| 35 mins ago | comment | added | Stefaan Vaes | Most of the time, in particular when all $p_n$ are equal, the measure $\mu$ is nonatomic. But the support is indeed the entire Cantor set. If $U \subset (\mathbb{Z}/Z\mathbb{Z})^{\mathbb{N}}$ is an open subset, there exists an $n \in \mathbb{N}$ and $x_1,\ldots,x_n \in \mathbb{Z}/Z\mathbb{Z}$ such that $\{x_1\} \times \cdots \times \{x_n\} \times (\mathbb{Z}/Z\mathbb{Z})^{[n+1,\infty)}$ is a subset of $U$, with strictly positive measure $\mu_1(x_1) \cdots \mu_n(x_n)$. | |
| 9 hours ago | vote | accept | Tomás Pacheco | ||
| 10 hours ago | comment | added | Tomás Pacheco | What a neat example, thank you! Just to make sure I followed, if we pick different $\lambda$'s we obtain different probability measures, all of which give non-zero measure to points, meaning the support is always the whole Cantor set, correct? | |
| yesterday | history | answered | Stefaan Vaes | CC BY-SA 4.0 |