Timeline for Can distribution theory be developed Riemann-free?
Current License: CC BY-SA 4.0
5 events
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| Feb 1, 2020 at 20:43 | comment | added | Abdelmalek Abdesselam | Indeed, these days I have to worry about continuity a lot because I do probability theory with random Schwartz distributions. Various constructions need to be Borel measurable, which often is simply due to continuity. | |
| Feb 1, 2020 at 14:38 | comment | added | paul garrett | @AbdelmalekAbdesselam, yes, nowadays when teaching I try to emphasize that although it was a superb insight of Schwartz to in one stroke define distributions as dual spaces, that mainly just give instant rigor to the idea of defining things by extension-by-continuity. | |
| Feb 1, 2020 at 0:01 | comment | added | Abdelmalek Abdesselam | Reminds me of how I unlearned my first impression of the distributional derivative. I first learned the notion this way: 1) write the paring as a formal integral, 2) do some heuristic integration by part, 3) realize that now you have something that makes sense rigorously, 4) use the latter as the rigorous definition. Now I prefer to view it as the unique extension of the classical derivative from say $\mathscr{S}$ to $\mathscr{S}'$. | |
| Jan 31, 2020 at 23:54 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| Jan 31, 2020 at 23:31 | history | answered | paul garrett | CC BY-SA 4.0 |