Timeline for What is the probability space that the CLT is really being applied to?
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20 at 9:51 | vote | accept | ac1501 | ||
| Jul 20, 2023 at 21:36 | comment | added | ac1501 | Thanks @whuber! I was familiar with this construction right up until where you say "The foregoing construction assures that any finite collection of these 𝐗𝑛 are independent." I assume you mean that the "lifted" $X_n$ are independent even if the original $X_n$ defined on $\Omega$ are not. I need to think about this a bit to convince myself... Also where you talk about the $F_n$ I would have thought the (vanilla) CLT expects those $F_n$ to be the same in order to be applicable. I assume you're saying the CLT applies if the "lifted" $X_n$ do, indeed, have identical distribution. | |
| Jul 20, 2023 at 18:54 | history | answered | whuber♦ | CC BY-SA 4.0 |