Timeline for Lower semi-continuity of integration
Current License: CC BY-SA 4.0
12 events
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| Jun 24, 2018 at 16:17 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Jun 21, 2018 at 16:50 | comment | added | ABIM | I don;t know this book. What is it called? | |
| Jun 21, 2018 at 1:38 | comment | added | Piotr Hajlasz | Did you check the book by Fonseca and Leoni? | |
| Jun 20, 2018 at 23:15 | comment | added | ABIM | True, in that case the most I can assume is that $f$ is convex in its second variable for almost-every $x$ (I made the update, as I was trying for a weaker result) | |
| Jun 20, 2018 at 23:14 | history | edited | ABIM | CC BY-SA 4.0 |
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| Jun 20, 2018 at 23:07 | comment | added | Nate Eldredge | Oh yeah, I missed "weak". But Borel is certainly not enough; take $f(x,u) = 1_{[0,1]}(u)$ and $u_n = 1+1/n$. | |
| Jun 20, 2018 at 23:05 | history | edited | ABIM | CC BY-SA 4.0 |
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| Jun 20, 2018 at 23:05 | comment | added | ABIM | Even under those assumptions, whouldn't that only give strong lower semi continuity which is less than weak lower semi continuity? | |
| Jun 20, 2018 at 23:02 | comment | added | Nate Eldredge | What are you assuming about $f$? If it's continuous in the second variable and nonnegative then this is just Fatou's lemma. And if it's not continuous then I don't see why you would expect any semicontinuity at all. | |
| Jun 20, 2018 at 22:50 | comment | added | ABIM | Aren't sequential weak lower-semi-continuity and weak lower-semi-continuity the same in a Hilbert space? | |
| Jun 20, 2018 at 22:42 | comment | added | Piotr Hajlasz | You should clarify what statement you have in mind. For example $\int_{\mathbb{R}^n}|u|^2$ is (sequentially) weakly lower semicontinuous since the norm is (sequentially) weakly lower semicontinuous. | |
| Jun 20, 2018 at 22:32 | history | asked | ABIM | CC BY-SA 4.0 |