Timeline for If every point is a Lebesgue point of $f$, is $f$ continuous a.e.?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 7, 2022 at 16:35 | comment | added | Sam Forster | Thanks for the details Pietro. It's also worth pointing out that "almost every discontinuous" is optimal in some sense. This is because if $f$ has Lebesgue points everywhere, then it is of Baire class one and hence continuous on a comeager set. In particular $f$ must be continuous at continuumly many points within every non-empty open interval. | |
| Sep 6, 2022 at 14:32 | history | edited | Pietro Majer | CC BY-SA 4.0 |
deleted 1 character in body
|
| Sep 6, 2022 at 13:40 | comment | added | Nate River | Thank you for the details! | |
| Sep 6, 2022 at 12:22 | history | answered | Pietro Majer | CC BY-SA 4.0 |