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.
@article{119216,
author = {Donatella Bongiorno and Udayan B. Darji and Washek Frank Pfeffer},
title = {On indefinite BV-integrals},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {41},
year = {2000},
pages = {843-853},
zbl = {1052.26006},
mrnumber = {1800159},
language = {en},
url = {http://dml.mathdoc.fr/item/119216}
}
Bongiorno, Donatella; Darji, Udayan B.; Pfeffer, Washek Frank. On indefinite BV-integrals. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 843-853. http://gdmltest.u-ga.fr/item/119216/
A constructive minimal integral which includes Lebesgue integrable functions and derivatives, J. London Math. Soc., to appear. | Zbl 0980.26006
The minimal integral which includes Lebesgue integrable functions and derivatives, Coll. Math. 50 (1986), 289-293. (1986) | MR 0857865 | Zbl 0604.26006
Variations of additive functions, Czechoslovak Math. J. 47 (1997), 525-555. (1997) | MR 1461431 | Zbl 0903.26004
A unified theory of integration, Amer. Math. Monthly 80 (1973), 349-359. (1973) | MR 0318434 | Zbl 0266.26008
The Riemann Approach to Integration, Cambridge Univ. Press, Cambridge, 1993. | MR 1268404 | Zbl 1143.26005
Comparing variations of charges, Indiana Univ. Math. J. 45 (1996), 643-654. (1996) | MR 1422100 | Zbl 0894.26004
On variations of functions of one real variable, Comment. Math. Univ. Carolinae 38.1 (1997), 61-71. (1997) | MR 1455470 | Zbl 0888.26006