Timeline for Discrepancy of the finite approximation of the Lebesgue measure
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 22, 2019 at 8:44 | comment | added | Fedor Petrov | @YCor yes, your understanding is correct, and Fedja's comment actually contains the answer: $a(N)$ behaves as $\log(N)/N$. | |
| May 22, 2019 at 8:43 | history | edited | Fedor Petrov | CC BY-SA 4.0 |
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| May 22, 2019 at 8:15 | comment | added | YCor | What is meant by "always"? for every $\mu$? is my understanding correct: for given $\mu$, define $b_\mu=\sup_R|\mu(R)-\lambda(R)|$, and $a(N)$ is defined as $\inf_\mu b_\mu$? | |
| May 22, 2019 at 7:44 | comment | added | fedja | Just look at pdfs.semanticscholar.org/a39e/… and references therein, if necessary, to get an idea of the current state of art. In dimension 2, the problem is settled completely, but in higher dimensions there is a gap between the powers of $\log$ in the lower and the upper bounds. | |
| May 22, 2019 at 7:42 | history | edited | YCor |
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| May 22, 2019 at 7:17 | history | asked | Fedor Petrov | CC BY-SA 4.0 |