Timeline for Is there a version of Fischer-Riesz theorem for Banach space?
Current License: CC BY-SA 4.0
8 events
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| Sep 21 at 20:40 | history | edited | Gerald Edgar | CC BY-SA 4.0 |
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| Sep 21 at 20:31 | comment | added | James E Hanson | Do you have a reference for the theorem of Charles Stegall? | |
| Jan 5, 2021 at 15:02 | comment | added | Pietro Majer | (Or is it just the fact f+g is not equal a.e. to any measurable function? ) | |
| Jan 5, 2021 at 14:41 | comment | added | Pietro Majer | A very nice example. Yet I don't see clearly what happens to the quotient of the space (which I would rather denote $\mathcal{L}_p$) of functions, modulo equivalence a.e. (i.e. the space of the classes of functions, which I would denote $L_p:=\mathcal{L}_p/\sim$ ). In the space $(\Omega,\mathcal{F},P)$ here, whatever is the probability $P$, the sigma-algebra $\mathcal{F}$ has uncountably many singletons, so some of them are null sets, and $L_p$ is not $\mathcal{L}_p$. Can we adapt the example to show $L^p(\Omega)$ (quotient) is not a vector space? | |
| Oct 26, 2018 at 15:02 | history | edited | Gerald Edgar | CC BY-SA 4.0 |
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| Oct 25, 2018 at 23:20 | comment | added | Nik Weaver | This looks right. | |
| Oct 25, 2018 at 23:16 | history | edited | Gerald Edgar | CC BY-SA 4.0 |
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| Oct 25, 2018 at 23:11 | history | answered | Gerald Edgar | CC BY-SA 4.0 |