Timeline for Why pi-systems and Dynkin/lambda systems? On the relative merits of approaches in measure theory.
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 13, 2018 at 11:13 | answer | added | Kostya_I | timeline score: 4 | |
| Aug 31, 2010 at 21:52 | answer | added | Nate Eldredge | timeline score: 6 | |
| Jul 20, 2010 at 17:59 | comment | added | Mark Meckes | I seem to recall, in fact, hearing someone say he'd taken measure theory from Dynkin as an undergraduate, then took it again without the $\pi-\lambda$ in grad school, and was surprised at how much more complicated it seemed the second time. | |
| Jul 20, 2010 at 17:57 | comment | added | Mark Meckes | I think this is nothing but a historical accident. I believe that Dynkin - a probabilist - proved the $\pi-\lambda$ theorem after the modern foundations of measure theory had been basically set up. Probabilists have, since then, used it in writing their textbooks, which are usually (at least presented as) books on probability as opposed to analysis. Analysis textbooks, on the other hand, are mostly written by functional analysts, harmonic analysts, PDEists, etc., who may never have opened a probability textbook, and so $\pi-\lambda$ systems have been slow to cross the divide. | |
| Jul 18, 2010 at 0:52 | answer | added | Peter Luthy | timeline score: 21 | |
| Jul 17, 2010 at 16:53 | comment | added | Bill Johnson | I also am puzzled, Spencer. When I teach Real Analysis, I use the $\pi$-$\lambda$ theorem even though the book we use does not mention it. | |
| Jul 17, 2010 at 15:44 | comment | added | Harry Gindi | These are incredibly useful in the strangest of places. On my measure theory midterm last year, there was a problem that was harder than our professor intended it to be. The problem came down to some nasty analysis where you had to come up with n separate bounds bounded by another bound. However, a friend of mine told us later that he came up with a beautiful concise proof using Dynkin systems (which was confirmed when he received full marks). | |
| Jul 17, 2010 at 15:07 | history | asked | Spencer | CC BY-SA 2.5 |