| Title:
|
On indefinite BV-integrals (English) |
| Author:
|
Bongiorno, D. |
| Author:
|
Darji, U. |
| Author:
|
Pfeffer, W. F. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
843-853 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present an example of a locally BV-integrable function in the real line whose indefinite integral is not the sum of a locally absolutely continuous function and a function that is Lipschitz at all but countably many points. (English) |
| Keyword:
|
BV integral |
| Keyword:
|
absolute continuity |
| Keyword:
|
pointwise Lipschitz functions |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| idZBL:
|
Zbl 1052.26006 |
| idMR:
|
MR1800159 |
| . |
| Date available:
|
2009-01-08T19:07:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119216 |
| . |
| Reference:
|
[1] Bongiorno B., Di Piazza L., Preiss D.: A constructive minimal integral which includes Lebesgue integrable functions and derivatives.J. London Math. Soc., to appear. Zbl 0980.26006 |
| Reference:
|
[2] Bruckner A.M., Fleissner R.J., Foran J.: The minimal integral which includes Lebesgue integrable functions and derivatives.Coll. Math. 50 (1986), 289-293. Zbl 0604.26006, MR 0857865 |
| Reference:
|
[3] Buczolich Z., Pfeffer W.F.: Variations of additive functions.Czechoslovak Math. J. 47 (1997), 525-555. Zbl 0903.26004, MR 1461431 |
| Reference:
|
[4] McShane E.J.: A unified theory of integration.Amer. Math. Monthly 80 (1973), 349-359. Zbl 0266.26008, MR 0318434 |
| Reference:
|
[5] Pfeffer W.F.: The Riemann Approach to Integration.Cambridge Univ. Press, Cambridge, 1993. Zbl 1143.26005, MR 1268404 |
| Reference:
|
[6] Pfeffer W.F.: Comparing variations of charges.Indiana Univ. Math. J. 45 (1996), 643-654. Zbl 0894.26004, MR 1422100 |
| Reference:
|
[7] Pfeffer W.F.: On variations of functions of one real variable.Comment. Math. Univ. Carolinae 38.1 (1997), 61-71. Zbl 0888.26006, MR 1455470 |
| . |
