Timeline for Convergence of iterated conditional expectations
Current License: CC BY-SA 4.0
9 events
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| Aug 2 at 15:04 | history | became hot network question | |||
| Aug 2 at 8:58 | answer | added | Jochen Glueck | timeline score: 5 | |
| Aug 2 at 7:40 | comment | added | Jochen Glueck | Ok, the other Jochen was a minute earlier. ;-) | |
| Aug 2 at 7:39 | comment | added | Jochen Glueck | One certainly has strong convergence in $L^2$. (This is true for general orthogonal projections on Hilbert space, not only for conditional expectations, and is, I think, also due to von Neumann. It should be quite straightforward to prove by using the spectral theorem for self-adjoint operators.) I don't know about the almost everywhere convergence, though. | |
| Aug 2 at 7:38 | comment | added | Jochen Wengenroth | Von Neumann's theorem about alternating orthogonal projections in Hilbert spaces yields $L^2$-convergence for $X\in L^2$. | |
| Aug 2 at 7:23 | history | edited | Nate River | CC BY-SA 4.0 |
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| Aug 2 at 7:17 | history | edited | Nate River | CC BY-SA 4.0 |
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| Aug 2 at 7:10 | history | edited | Nate River | CC BY-SA 4.0 |
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| Aug 2 at 7:03 | history | asked | Nate River | CC BY-SA 4.0 |