Timeline for Two definitions of $L^p$ spaces that are not always equivalent
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 8, 2020 at 19:00 | comment | added | LSpice | The name of the linked paper by Kelley: Decomposition and representation theorems in measure theory. | |
| Jun 8, 2020 at 18:17 | comment | added | Dmitri Pavlov | @ogogmad: This is Theorem 2 in Kelley's paper that is linked in the answer. | |
| Jun 8, 2020 at 18:16 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
added 32 characters in body
|
| Jun 8, 2020 at 18:10 | comment | added | wlad | Can you link to a reference to your Hahn-Jordan decomposition theorem? | |
| Jun 8, 2020 at 17:58 | comment | added | Dmitri Pavlov | @ogogmad: First of all, the Lebesgue decomposition theorem does not require σ-finiteness or any other conditions (see the nLab). Secondly, as I already explained, it has nothing to do with the Hahn–Jordan decomposition, which decomposes a signed measure into its positive and negative components. | |
| Jun 8, 2020 at 17:52 | comment | added | wlad | Wikipedia says that Lebesgue decomposition requires that the measures $\mu$ and $\nu$ be $\sigma$-finite. This can surely be relaxed, but it doesn't hold unconditionally | |
| Jun 8, 2020 at 17:49 | comment | added | Dmitri Pavlov | @ogogmad: No. I am not even sure what you are trying to say here, since the Lebesgue decomposition theorem is trivial in the case of absolute continuity, which is a precondition for the Hahn–Jordan theorem. | |
| Jun 8, 2020 at 17:32 | comment | added | wlad | Sounds like the Lebesgue decomposition theorem, no? | |
| Jun 8, 2020 at 15:32 | comment | added | Dmitri Pavlov | @ogogmad: It's a different Hahn–Jordan decomposition theorem (one measure instead of two). I added a clarification. | |
| Jun 8, 2020 at 15:30 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
added 60 characters in body
|
| Jun 8, 2020 at 6:47 | comment | added | wlad | The Hahn-Jordan decomposition theorem is stated on Wikipedia without any preconditions | |
| Jun 8, 2020 at 1:20 | review | Suggested edits | |||
| Jun 8, 2020 at 2:03 | |||||
| Jun 7, 2020 at 20:27 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
added 214 characters in body
|
| Jun 7, 2020 at 20:07 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |