Timeline for Why should one still teach Riemann integration?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 29, 2019 at 2:36 | comment | added | reuns | I think in complex analysis it is unnatural to look at Lebesgue's integral because every function is continuous away from a few points and in contrary to the improper Riemann integral it doesn't fit well with the residue theorem and the local uniformly convergent sequences proving the analyticity. | |
| Jan 8, 2013 at 20:39 | comment | added | Toby Bartels | Since we only need integrals of continuous functions, we could equally well use the Cauchy integral. | |
| Jan 21, 2011 at 16:18 | comment | added | Keenan Kidwell | When I first read Rudin's Real and Complex Analysis I found his "construction" of Lebesgue measure on $\mathbb{R}^n$, where he essentially applies the Riesz Representation Theorem to the functional given by the Riemann integral, hard to understand. I personally find Folland's approach of constructing Borel measures on $\mathbb{R}$ from increasing, right continuous functions and then taking products to get Lebesgue measure on $\mathbb{R}^n$ more intuitive and less "magical." | |
| Jan 21, 2011 at 10:15 | comment | added | Ketil Tveiten | Definitions of the type "the unique [thing] that [makes it work]" are very bad pedagogically, even if they are nice for theory-building. The obvious fix in your case would be to use the usual definition (you know, length of intervals etc.). | |
| Jan 21, 2011 at 7:48 | history | answered | Stefan Geschke | CC BY-SA 2.5 |