| Title:
|
A descriptive definition of a BV integral in the real line (English) |
| Author:
|
Caponetti, Diana |
| Author:
|
Marraffa, Valeria |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
421-432 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A descriptive characterization of a Riemann type integral, defined by BV partition of unity, is given and the result is used to prove a version of the controlled convergence theorem. (English) |
| Keyword:
|
pseudopartition |
| Keyword:
|
strong Luzin condition |
| Keyword:
|
bounded variation |
| Keyword:
|
Riemann type integral |
| Keyword:
|
controlled convergence theorem |
| Keyword:
|
ACG$^\circ$ |
| Keyword:
|
ACG$^\circ$ |
| MSC:
|
26A39 |
| MSC:
|
26A45 |
| idZBL:
|
Zbl 0936.26004 |
| idMR:
|
MR1722876 |
| DOI:
|
10.21136/MB.1999.125999 |
| . |
| Date available:
|
2009-09-24T21:39:24Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125999 |
| . |
| Reference:
|
[1] B. Bongiorno L. Di Piazza: Convergence theorems for generalized Riemann-Stieltjes integrals.Real Anal. Exchange 11 (1991-92), 339-361. MR 1147373 |
| Reference:
|
[2] B. Bongiorno M. Giertz W. F. Pfeffer: Some nonabsolutely convergent integrals in the real line.Boll. Un. Mat. Ital. B (7) 6 (1992), 371-402. MR 1171108 |
| Reference:
|
[3] B. Bongiorno W. F. Pfeffer: A concept of absolute continuity and a Riemann type integral.Comment. Math. Univ. Carolin. 33 (1992), 184-196. MR 1189651 |
| Reference:
|
[4] D. Caponetti V. Marraffa: An integral in the real line defined by BV partitions of unity.Atti Sem. Mat. Fis. Univ. Modena 42 (1994), 69-82. MR 1282323 |
| Reference:
|
[5] J. Kurzweil J. Mawhin W. F. Pfeffer: An integral defined by approximating BV partitions of unity.Czechoslovak Math. J. 41 (1991), 695-712. MR 1134958 |
| Reference:
|
[6] P. Y. Lee: On ACG* functions.Real Anal. Exchange IS (1989-90), 754-759. MR 1059436 |
| Reference:
|
[7] W. F. Pfeffer: The Gauss-Green theorem.Adv. Math. 87 (1991), 93-147. Zbl 0732.26013, MR 1102966, 10.1016/0001-8708(91)90063-D |
| Reference:
|
[8] W. F. Pfeffer: A descriptive definition of a variational integral.Proc. Amer. Math. Soc. 114 (1992), 99-106. MR 1072090, 10.1090/S0002-9939-1992-1072090-2 |
| Reference:
|
[9] W. F. Pfeffer: The Riemann Approach to Integration.Cambridge Univ. Press, Cambridge, 1993. Zbl 0804.26005, MR 1268404 |
| . |
