Timeline for Approximating arbitrary probability measures by discrete ones
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2021 at 22:24 | comment | added | TOM | I am sorry for the late reply. I could not make it work, but found a roundabout that was enough for my purposes. | |
| May 26, 2021 at 11:59 | comment | added | Brendan McKay | Actually I'm not so sure that what I wrote is true. Have you checked if it works? | |
| May 26, 2021 at 0:53 | comment | added | TOM | Thank you for your answers - it is most useful! | |
| May 22, 2021 at 11:50 | comment | added | Brendan McKay | Maybe smaller cubes are needed so that balls centred nearby will cover them. Hopefully you can work out the details. | |
| May 22, 2021 at 11:16 | comment | added | Brendan McKay | (For second version) Partition $\mathbb{R}^d$ into cubes of side $d^{-1/2}$. Choose cubes in decreasing order of $\mu$ measure until their total measure exceeds $1-\varepsilon$. That only takes a finite number of choices, since the sequence converges. Now support your discrete measure on the centres of the selected cubes. | |
| May 22, 2021 at 10:19 | history | edited | TOM | CC BY-SA 4.0 |
added 192 characters in body
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| May 22, 2021 at 10:14 | comment | added | TOM | Thank you, I will mend the question as I need a weaker statement, but hoped that something stronger could be true, but it turned out to be naive. | |
| May 22, 2021 at 9:49 | answer | added | reliquia | timeline score: 1 | |
| May 22, 2021 at 9:35 | comment | added | Brendan McKay | Take $\mu$ to be the normal distribution on the real line and $\nu$ to be supported on a finite set $X$. The complement $A$ of $X$ is open yet $\mu(A)=1$ and $\nu(A)=0$. | |
| May 22, 2021 at 9:02 | history | asked | TOM | CC BY-SA 4.0 |