Timeline for Convergence of iterated conditional expectations
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 2 at 14:10 | comment | added | Nate River | ... I missed that $\mathbb E_{\mathcal G} \mathbb E_{\mathcal G} = \mathbb E_{\mathcal G}$. Nice! | |
| Aug 2 at 13:42 | comment | added | Jochen Glueck | @NateRiver: The functions $P_1^n X$ are the elements of your sequence with the odd indices and the functions $P_2^n \mathbb{E}_{\mathcal{H}} X$ are the elements of your sequence with the even indices. If the "odd" and the "even" subsequence both converge almost everywhere to the same function, the entire sequence converges almost everywhere. | |
| Aug 2 at 11:23 | comment | added | Nate River | Thanks for the answer! I may be missing something obvious, but how does one obtain the final conclusion from the fact that the two limits coincide? | |
| Aug 2 at 8:58 | history | answered | Jochen Glueck | CC BY-SA 4.0 |