| Title:
|
A full descriptive definition of the BV-integral (English) |
| Author:
|
Bongiorno, B. |
| Author:
|
Di Piazza, L. |
| Author:
|
Pfeffer, W. F. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
461-469 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a Cauchy test for the almost derivability of additive functions of bounded BV sets. The test yields a full descriptive definition of a coordinate free Riemann type integral. (English) |
| Keyword:
|
Perimeter |
| Keyword:
|
partition |
| Keyword:
|
gage |
| Keyword:
|
absolute continuity |
| MSC:
|
26A39 |
| MSC:
|
26B30 |
| MSC:
|
28A75 |
| idZBL:
|
Zbl 0842.26009 |
| idMR:
|
MR1364486 |
| . |
| Date available:
|
2009-01-08T18:19:20Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118774 |
| . |
| Reference:
|
[1] Bongiorno B.: Differentiation of set functions.Rend. Circ. Mat. Palermo 26 37-51 (1977). Zbl 0399.28003, MR 0524331 |
| Reference:
|
[2] Evans L.C., Gariepy R.F.: Measure Theory and Fine Properties of Functions.CRC Press, Boca Raton, 1992. Zbl 0804.28001, MR 1158660 |
| Reference:
|
[3] Kurzweil J., Jarník J.: Equi-integrability and controlled convergence of Perron-type integrable functions.Real Anal. Ex. 17 110-139 (1991:92). MR 1147361 |
| Reference:
|
[4] Pfeffer W.F.: A descriptive definition of a variational integral and applications.Indiana Univ. Math. J. 40 259-270 (1991). Zbl 0747.26010, MR 1101229 |
| Reference:
|
[5] Pfeffer W.F.: The Gauss-Green theorem.Adv. Math. 87 93-147 (1991). Zbl 0732.26013, MR 1102966 |
| Reference:
|
[6] Pfeffer W.F.: The Riemann Approach to Integration.Cambridge Univ. Press, Cambridge, 1993. Zbl 1143.26005, MR 1268404 |
| Reference:
|
[7] Saks S.: Theory of the Integral.Dover, New York, 1964. Zbl 0017.30004, MR 0167578 |
| Reference:
|
[8] Volpert A.I.: The spaces BV and quasilinear equations.Math. USSR-SB. 2 255-267 (1967). MR 0216338 |
| . |
