Timeline for On the uniform boundedness principle and the space of functions of bounded variation
Current License: CC BY-SA 4.0
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| Jan 28, 2021 at 18:26 | comment | added | mlk | Not sure if I understand your question. But as a note, among sufficiently smooth functions of compact support, $\operatorname{div} \phi = \psi$ has a solution $\phi$ precisely if $\int \psi \,dm = 0$. In other words (A) characterizes weak convergence modulo averages. Thus denoting $C_f := \int f dm$, we have that (A) is true if and only if $(f_n-C_{f_n}) \,dm \to (f - C_f)\, dm$ in the sense of measures. Also note that if (A) holds for some $f$, then it also holds for any $f+a$, $a \in \mathbb{R}$ without changing the $f_n$. | |
| Jan 27, 2021 at 23:17 | history | undeleted | sharpe | ||
| Jan 27, 2021 at 22:56 | history | deleted | sharpe | via Vote | |
| Jan 27, 2021 at 22:09 | history | edited | sharpe | CC BY-SA 4.0 |
added 9 characters in body
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| Jan 27, 2021 at 20:05 | history | asked | sharpe | CC BY-SA 4.0 |