Timeline for Quantitative Borel-Cantelli
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 12, 2023 at 16:07 | vote | accept | JustSomeGuy | ||
| Aug 12, 2023 at 13:46 | history | became hot network question | |||
| Aug 12, 2023 at 8:52 | comment | added | Pietro Majer | I would say, if we fix a number $n$, then there is a $B_n$ with $p(B_n)\ge 1-2\delta$ such that any $x\in B_n$ belongs to $A_k$ for al least $(1-2\delta)n$ indices $k\le n$. So points in $B_*:=\liminf B_n$ belong to the $A_k$'s for a set of indices $k$ with lower density al least $1-2\delta$, but $B_*$ may be a null set. The set $B^*:=\limsup B_n$ has again $p(B^*)\ge 1-2\delta$, and points in $B^*$ belong to the $A_k$'s with upper density al least $1-2\delta$. | |
| Aug 12, 2023 at 7:51 | answer | added | Fedor Petrov | timeline score: 4 | |
| Aug 12, 2023 at 7:19 | comment | added | Jochen Wengenroth | You need the independence of the events $A_n$ and then $p(\lim\sup A_n)=1$. | |
| Aug 12, 2023 at 5:45 | history | asked | JustSomeGuy | CC BY-SA 4.0 |