Green's theorem with no differentiability
| dc.creator | Fleischer, I. | |
| dc.date | 2002-11-25 | |
| dc.date | 2003-02-24 | |
| dc.date.accessioned | 2026-07-07T04:53:16Z | |
| dc.date.available | 2026-07-07T04:53:16Z | |
| dc.description | The result is established for a Jordan measurable region with rectifiable boundary. The integrand F for the new plane integral to be used is a function of axis-parallel rectangles, finitely additive on non-overlapping ones, hence unambiguously defined and additive on "figures" (i.e. finite unions of axis-parallel rectangles). Define its integral over Jordan measurable S as the limit of its value on the figures, which contain a subfigure of S and are contained in a figure containing S, as the former/complements of the latter expand directedly to fill out S/the complement of S. The integral over every Jordan measurable region exists when additive F is "absolutely continuous" in the sense of converging to zero as the area enclosed by its argument does, or with F the circumferential line integral $\oint P dx + Q dy$ for $P$, $Q$ continuous at the rectifiable boundary of S and integrable along axis - parallel line segments. Thus the equality of this area integral with the line integral around the boundary, to be proved, follows for the various integrals of divergence presented in: Pfeffer, W.F. The Riemann Approach to Integration, Cambridge Univ. Press, New York, 1993. | |
| dc.description | 5 pages, no figures green.tex is an AMS-TeX file. To process, run the command > amstex green.tex | |
| dc.identifier | https://arxiv.org/abs/math/0211393 | |
| dc.identifier | http://arxiv.org/abs/math/0211393 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65780 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Green's theorem with no differentiability | |
| dc.type | text |