Timeline for Weak convergence + convergence of the norm implies strong convergence in Orlicz spaces
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 2 at 21:49 | vote | accept | leo monsaingeon | ||
| Apr 2 at 19:01 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Typo fixes minor additions
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| Apr 2 at 18:45 | answer | added | rpk | timeline score: 5 | |
| Nov 24, 2023 at 23:10 | history | became hot network question | |||
| Nov 24, 2023 at 21:34 | comment | added | leo monsaingeon | @erz thank you, I was not aware that this had a name. good to know! | |
| Nov 24, 2023 at 21:03 | answer | added | Ayman Moussa | timeline score: 6 | |
| Nov 24, 2023 at 17:16 | comment | added | erz | let me just mention that this property is known as Kadets-Klee or Radon-Riesz property | |
| Nov 24, 2023 at 16:19 | comment | added | Akira | Thank you so much for your elaboration! | |
| Nov 24, 2023 at 16:18 | comment | added | leo monsaingeon | Let me just give a heuristic reasoning as to why this may hold true: it is well known that lack of strong convergence can only arise form oscillations. But, wild oscillations tend to encode lots of information in the sense of 1/0 bits in information theory. Such bits correspond to high entropy. But since $\limsup E(\rho_n)\leq E(\rho)$ the sequence cannot contain too much information, thus it should not oscillate too fast, and converge better than expected. OK sure, this is a very very rough picture, but I think there's some truth to it and I'm trying to make put this intuition on solid ground | |
| Nov 24, 2023 at 16:12 | comment | added | leo monsaingeon | Well, that's the whole point: for some independent reason I'm able to prove that the entropy converges. and I want to improve the convergence, i-e $\rho_n\to\rho$ should hold in a stronger sense than I initially assumed. | |
| Nov 24, 2023 at 16:09 | comment | added | Akira | The Boltzmann entropy is only l.s.c. in the weak topology of $L^1 (\Omega)$. Do you have some situations where we have the convergence $\int_\Omega \rho_n(x)\log\rho_n(x) \mathrm d x\to \int_\Omega \rho(x)\log\rho(x) \mathrm d x$? | |
| Nov 24, 2023 at 15:07 | history | asked | leo monsaingeon | CC BY-SA 4.0 |