Timeline for Blackbox Theorems
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 28, 2012 at 11:56 | comment | added | Emilio Pisanty | @EvanJenkins: do you have a reference for the non-AC proof? When studying Haar measure construction I found a lot of texts doing only the compact case, and one text with an AC proof of the locally compact case. | |
| Jun 15, 2012 at 17:44 | comment | added | Evan Jenkins | What is not terribly well known (or exposited in very many books) is the constructive proof of existence and uniqueness of Haar measure that does not use the axiom of choice. While I imagine the vast majority of people who make use of Haar measure either don't care about the axiom of choice or have nicer constructions as Ben Wieland suggests, it is at very least an interesting curiosity that the axiom of choice is not needed at all, since the usual proof one sees relies so crucially on it. | |
| Jun 15, 2012 at 5:46 | comment | added | Yemon Choi | That said, I agree that this example doesn't really fit Benjamin Steinberg's original requirement. | |
| Jun 15, 2012 at 4:08 | comment | added | Yemon Choi | Again, in mild dissent from the previous comments, I have seen a fair number of papers where $L^1(G)$ is name-checked by people who are not au fait with the proofs of existence and uniqueness for Haar, apart from some hasty revision for qualifying exams or similar. | |
| Jun 15, 2012 at 1:28 | comment | added | Felix Goldberg | Actually, the proof is quite widely available. | |
| Jun 14, 2012 at 2:11 | comment | added | Benjamin Steinberg | I think that probably most people in harmonic analysis more or less know how it works (as compared to the classification of finite simple groups). | |
| Jun 14, 2012 at 1:13 | comment | added | Ben Wieland | This is pretty easy to avoid in practice. eg, Haar measure on a manifold is easily constructed using invariant differential forms. Similarly, differential forms lift measure from $\mathbb Q_p$ to $p$-adic groups. Adeles are a little trickier (eg, naive choices on $G_m(A)$ yield the zero measure). | |
| Jun 13, 2012 at 23:25 | history | answered | Abhishek Parab | CC BY-SA 3.0 |