Timeline for Why is Lebesgue integration taught using positive and negative parts of functions?
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
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| Feb 20 at 8:08 | comment | added | Pietro Majer | As a student, I learnt integration by this approach: first Bochner integral for functions on abstract measure spaces, then non-negative measurable functions as a corollary. My final impression was: no bad after all, but the "truth" is likely to be the opposite: non-negative case is definitely of basic importance, and should better be the starting point. Starting with vector valued functions via Cauchy sequences seemed to me only due to a kind of algebraic aestheticism! | |
| Jun 24, 2011 at 22:53 | vote | accept | KConrad | ||
| Jun 10, 2011 at 12:56 | answer | added | Piero D'Ancona | timeline score: 6 | |
| May 19, 2010 at 23:00 | comment | added | KConrad | In Lang's treatment, the monotone convergence theorem and Fatou's lemma play a comparatively minor role in the foundational development, which might seem very strange to the analysts. But at the end of the day his book produces all the same basic theorems, and he has an exercise on non-negative functions to show the traditional approach via suprema of simple non-negative functions produces the same completion as the approach used in his book. | |
| May 19, 2010 at 8:21 | answer | added | Sergei Ivanov | timeline score: 29 | |
| May 19, 2010 at 4:51 | comment | added | Victor Protsak | Isn't it true that Lang was just following the Bourbaki approach? | |
| May 19, 2010 at 4:11 | comment | added | Peter Luthy | Fatou's lemma is pretty useful. | |
| May 19, 2010 at 1:10 | answer | added | Carl Offner | timeline score: 53 | |
| May 18, 2010 at 20:26 | answer | added | Andrea Ferretti | timeline score: 7 | |
| May 18, 2010 at 19:28 | answer | added | Fabrizio Polo | timeline score: 14 | |
| May 18, 2010 at 18:51 | answer | added | Mark Meckes | timeline score: 4 | |
| May 18, 2010 at 18:49 | answer | added | Bill Johnson | timeline score: 10 | |
| May 18, 2010 at 18:49 | answer | added | coudy | timeline score: 11 | |
| May 18, 2010 at 18:29 | history | asked | KConrad | CC BY-SA 2.5 |