Timeline for Can Birkhoff's ergodic theorem for integrable functions easily be deduced from Birkhoff's ergodic theorem for bounded functions?
Current License: CC BY-SA 4.0
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| Jun 25 at 8:11 | comment | added | No-one | For completeness let me point out that this is called Banach Principle and is proved e.g. at page 214 of the book "Operator Theoretical Aspects of Ergodic Theory" by Eisner et al. | |
| Oct 23, 2021 at 23:29 | comment | added | Julian Newman | Thank you, this is very nice! By slightly adapting this, I think I can now get a full proof of Birkhoff's ergodic theorem that only requires adding about two to four lines to the proof I gave in the question for the bounded case. | |
| Oct 22, 2021 at 5:56 | history | answered | Anthony Quas | CC BY-SA 4.0 |