Timeline for Riemann Integral of Banach space valued functions
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 1, 2016 at 20:38 | comment | added | Liviu Nicolaescu | See Sec. V.3 on Bochner integral in Yosida's book ``Functional Analysis''. | |
| Jan 1, 2016 at 20:19 | comment | added | Pietro Majer | As a slightly different elementary theory, you may like the Cauchy integral for Banach valued regulated functions (that is, functions that have left and right limit at any point). See Dieudonné's "Foundations of modern analysis". | |
| Jan 1, 2016 at 18:04 | answer | added | mkk030572 | timeline score: 0 | |
| Feb 5, 2011 at 23:58 | comment | added | Zen Harper | No, I don't know a reference. But, to sketch an answer for the implied question you didn't ask, it's relatively easy if the Banach space valued function $f:[0,1] \to E$ is continuous (the norm topology throughout). The convex hull of the compact set $f([0,1]) \subset E$ has compact closure; now directly use a sequence of approximating Riemann sums $\sum_j f(t_j) (t_{j+1}-t_j)$; each one of these is, of course, a convex combination. Filling in the details is a fun exercise...! (It was several years ago when I worked out these details, so apologies if I've misremembered them.) | |
| Feb 5, 2011 at 18:56 | comment | added | Willie Wong | You may also want to take a look at the answers to this question: mathoverflow.net/questions/47721/… | |
| Feb 5, 2011 at 18:42 | answer | added | Daniel Pape | timeline score: 1 | |
| Feb 5, 2011 at 17:58 | history | asked | dingbar posak | CC BY-SA 2.5 |