Timeline for Integrals from a non-analytic point of view
Current License: CC BY-SA 2.5
4 events
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| Sep 12, 2010 at 19:47 | comment | added | Paul Siegel | I'm at best marginally familiar with Harrison's work as well, but in my experience calculus over non-smooth spaces generally only works almost everywhere relative to some measure. In particular it requires additional assumptions (e.g. curvature bounds in the sense of Alexandrov geometry) and hard work to prove theorems about the topology of non-smooth spaces. Harrison's techniques are different from what I'm used to though, so I can't be sure. | |
| Sep 12, 2010 at 19:16 | comment | added | Theo Johnson-Freyd | I don't know much about the work of Jenny Harrison, but I think that she does have a theory of differential forms, etc., for quite non-smooth spaces. I could be wrong, though; if you (or another reader here) know(s) her work, maybe you can comment on it? | |
| Sep 12, 2010 at 17:37 | comment | added | Paul Siegel | One more thing. You might be interested in the following note: maths.gla.ac.uk/~tl/glasgowpssl/banach.pdf if you would like the Lebesgue integral to appear more natural (in more ways than one). While the punchline may seem profound at first, there isn't actually much serious content. | |
| Sep 12, 2010 at 16:18 | history | answered | Paul Siegel | CC BY-SA 2.5 |