Timeline for Continuity of $r\mapsto\int_{\Sigma\cap B_r(x)}f^2d\mu$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2020 at 14:28 | comment | added | Pierre PC | I don't know that it's commonly used. If the sum of non-negative terms over an arbitrary set is convergent, then only countably many of them are positive (S = indices of terms $>\varepsilon$); a compact operator has at most countably many eigenvalues, with at most one limit point (S = eigenvalues with modulus $>\varepsilon$); a discrete closed set of $\mathbb R^d$ is countable (S = elements with norm $\leq R$). I guess it is useful enough to be found here and there, but not sophisticated enough to have a name. | |
| Apr 7, 2020 at 8:10 | comment | added | Anonymous amateur | Thanks so much for the detailed answer. One soft question: Is this particular trick of considering $S_{\epsilon, R}$ (or its variations) commonly used in analysis? I feel that it may be useful in certain context.... | |
| Apr 7, 2020 at 8:06 | vote | accept | Anonymous amateur | ||
| Apr 4, 2020 at 21:48 | history | answered | Pierre PC | CC BY-SA 4.0 |