Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.22930 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910683311898624 |
|---|---|
| author | Jahel, Colin Perruchaud, Pierre |
| author_facet | Jahel, Colin Perruchaud, Pierre |
| contents | The classical de Finetti Theorem classifies the $\mathrm{Sym}(\mathbb N)$-invariant probability measures on $[0,1]^{\mathbb N}$. More precisely it states that those invariant measures are combinations of measures of the form $ν^{\otimes\mathbb N}$ where $ν$ is a measure on $[0,1]$. Recently, Jahel--Tsankov generalized this theorem showing that under conditions on $M$, the group $\operatorname{Aut}(M)$ is de Finetti, i.e. $\operatorname{Aut}(M)$-invariant measures on $[0,1]^M$ are mixtures of measures of the form $ν^{\otimes M}$ where $ν$ is a measure on $[0,1]$. In this note, we give an example of a non-de Finetti non-Archimedean group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A non-de Finetti theorem for countable Euclidean spaces Jahel, Colin Perruchaud, Pierre Probability Logic 37A50, 03C15 The classical de Finetti Theorem classifies the $\mathrm{Sym}(\mathbb N)$-invariant probability measures on $[0,1]^{\mathbb N}$. More precisely it states that those invariant measures are combinations of measures of the form $ν^{\otimes\mathbb N}$ where $ν$ is a measure on $[0,1]$. Recently, Jahel--Tsankov generalized this theorem showing that under conditions on $M$, the group $\operatorname{Aut}(M)$ is de Finetti, i.e. $\operatorname{Aut}(M)$-invariant measures on $[0,1]^M$ are mixtures of measures of the form $ν^{\otimes M}$ where $ν$ is a measure on $[0,1]$. In this note, we give an example of a non-de Finetti non-Archimedean group. |
| title | A non-de Finetti theorem for countable Euclidean spaces |
| topic | Probability Logic 37A50, 03C15 |
| url | https://arxiv.org/abs/2410.22930 |