Timeline for Can we say that: $ \sum_{n\geq 1}{\frac{1}{n}(f_n(\omega)-g_n(\omega))}<\infty\qquad a.e $
Current License: CC BY-SA 4.0
7 events
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| May 19, 2020 at 6:25 | history | edited | leo monsaingeon | CC BY-SA 4.0 |
removed the [lebesgue-measure] tag
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| May 19, 2020 at 4:37 | answer | added | Yuval Peres | timeline score: 4 | |
| May 19, 2020 at 4:22 | comment | added | Yuval Peres | The argument you suggest seems to assume a bound on $\|f_n\|_1$ rather than $\|f_n\|_\infty$. | |
| May 19, 2020 at 4:01 | comment | added | Parc John | We have $\sup_n\|f_n\|_1<\infty$. Then, there exists $n_0\in\mathbb{N}$, such that: for all $n\geq 1$ we have $$|f_n|\leq n_0~~ a.e.~$$Then, for all $n\geq n_0$: $$F_n(f_n)=f_n$ hence, we have the desired result. | |
| May 19, 2020 at 1:36 | review | First posts | |||
| May 19, 2020 at 6:26 | |||||
| May 19, 2020 at 1:35 | history | edited | Parc John | CC BY-SA 4.0 |
added 6 characters in body
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| May 19, 2020 at 1:27 | history | asked | Parc John | CC BY-SA 4.0 |