| Title:
|
A concept of absolute continuity and a Riemann type integral (English) |
| Author:
|
Bongiorno, B. |
| Author:
|
Pfeffer, W. F. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
189-196 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a descriptive definition of a multidimensional generalized Riemann integral based on a concept of generalized absolute continuity for additive functions of sets of bounded variation. (English) |
| Keyword:
|
sets of bounded variation |
| Keyword:
|
partitions |
| Keyword:
|
gages |
| Keyword:
|
generalized absolute continuity |
| MSC:
|
26A39 |
| MSC:
|
26B15 |
| MSC:
|
26B30 |
| idZBL:
|
Zbl 0776.26011 |
| idMR:
|
MR1189651 |
| . |
| Date available:
|
2009-01-08T17:54:59Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118488 |
| . |
| Reference:
|
[B-Gi-P] Bongiorno B., Giertz M., Pfeffer W.F.: Some nonabsolutely convergent integrals in the real line.to appear. Zbl 0774.26003, MR 1171108 |
| Reference:
|
[Fe] Federer H.: Geometric Measure Theory.Springer-Verlag New York (1969). Zbl 0176.00801, MR 0257325 |
| Reference:
|
[Go] Gordon R.: A descriptive characterization of the generalized Riemann integral.Real Analysis Exchange 15:1 (1989-1990), 397-400. Zbl 0703.26009, MR 1042557 |
| Reference:
|
[M-M] Massari U., Miranda M.: Minimal Surfaces in Codimension One.North-Holland Amsterdam (1984). MR 0795963 |
| Reference:
|
[PP1] Pfeffer W.F.: An integral in geometric measure theory.to appear. Zbl 0797.26007, MR 1225672 |
| Reference:
|
[PP2] Pfeffer W.F.: A Riemann type definition of a variational integral.Proc. American Math. Soc. 114 (1992), 99-106. Zbl 0749.26006, MR 1072090 |
| Reference:
|
[PP3] Pfeffer W.F.: A descriptive definition of a variational integral and applications.Indiana Univ. J. 40 (1991), 259-270. Zbl 0747.26010, MR 1101229 |
| Reference:
|
[PP4] Pfeffer W.F.: The Gauss-Green theorem.Adv. Math. 87 (1991), 93-147. Zbl 0732.26013, MR 1102966 |
| Reference:
|
[S] Saks S.: Theory of the Integral.Dover New York (1964). MR 0167578 |
| Reference:
|
[V] Volpert A.I.: The spaces $BV$ and quasilinear equations.Mathematics USSR-Sbornik 2 (1967), 225-267. MR 0216338 |
| . |
