User Tools
world:de-finetti
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | |||
|
world:de-finetti [2026/02/07 10:34] rdouc |
world:de-finetti [2026/02/07 12:44] (current) rdouc |
||
|---|---|---|---|
| Line 8: | Line 8: | ||
| <WRAP center round tip 80%> | <WRAP center round tip 80%> | ||
| **De Finetti's Theorem:** | **De Finetti's Theorem:** | ||
| - | Let $(X_i)_{i\in\mathbb{N}}$ be a family of **exchangeable random elements** taking balues on a measurable space $(\mathsf{X},\mathcal{X})$. Then, there exists a $\sigma$-field $\mathcal{G}_\infty$ such that, **conditionally on $\mathcal{G}_\infty$**, the random variables $(X_i)_{i\in\mathbb{N}}$ are **independent and identically distributed (i.i.d.)**. | + | Let $(X_i)_{i\in\mathbb{N}}$ be a family of **exchangeable random elements** taking values on a measurable space $(\mathsf{X},\mathcal{X})$. Then, there exists a $\sigma$-field $\mathcal{G}_\infty$ such that, **conditionally on $\mathcal{G}_\infty$**, the random variables $(X_i)_{i\in\mathbb{N}}$ are **independent and identically distributed (i.i.d.)**. |
| </WRAP> | </WRAP> | ||
world/de-finetti.txt · Last modified: 2026/02/07 12:44 by rdouc
Page Tools
