Timeline for Weak convergence of probability measures on the one-point compactification of $[0,\infty)$
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| May 30, 2021 at 18:34 | comment | added | user128095 | Done. Thanks again for your kindness | |
| May 30, 2021 at 18:34 | vote | accept | CommunityBot | ||
| May 30, 2021 at 18:34 | vote | accept | CommunityBot | ||
| May 30, 2021 at 18:34 | |||||
| May 30, 2021 at 18:23 | comment | added | Iosif Pinelis | @Neymar : From mathoverflow.net/help/someone-answers "To mark an answer as accepted, click on the check mark beside the answer to toggle it from greyed out to filled in." See e.g. mathoverflow.net/questions/394059/… for an illustration. You may also want to read here: mathoverflow.net/help/accepted-answer | |
| May 30, 2021 at 5:36 | comment | added | user128095 | Absolutely. What should I do such that the answer is accepted? | |
| May 30, 2021 at 2:14 | comment | added | Iosif Pinelis | @Neymar : So, are you satisfied with this answer? | |
| May 28, 2021 at 10:00 | comment | added | user128095 | Many thanks for the reply | |
| May 27, 2021 at 22:34 | comment | added | Iosif Pinelis | @Neymar : I have now provided all the details. | |
| May 27, 2021 at 22:34 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 27, 2021 at 12:34 | comment | added | Iosif Pinelis | @Neymar : (i) I don't know references concerning precisely this situation. (ii) To define continuous functions on a set $X$, one does not need to have a metric on $X$; to do that, it is sufficient (and necessary) to have a topology on $X$. In your case, of $X=[0,\infty]$, you defined the corresponding standard topology in your post. (iii) Still, if you wish, you can define a metric on $[0,\infty]$ say by the formula $d(x,y):=|g(x)-g(y)|$, where $g(x):=x/(1+x)$ for $x\in[0,\infty)$ and $g(\infty):=1$. | |
| May 27, 2021 at 12:25 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 27, 2021 at 8:41 | comment | added | user128095 | Thanks for the response. Is there any reference for the probability measures on the one-point compactification of $[0,\infty)$? Indeed, according to the definition of the one-point compactification, what is the corresponding metric and what are the corresponding continuous functions on $[0,\infty]$ (to define the weak convergence of 1)? | |
| May 27, 2021 at 3:15 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |