Article
Keywords:
multiplier; $C$-integral; $BV$ function
Summary:
We use an elementary method to prove that each $BV$ function is a multiplier for the $C$-integral.
References:
[1] B. Bongiorno:
A new integral for the problem of primitives. Matematiche (Catania) 51 (1996 1997), 299–313. (Italian)
MR 1488074
[3] B. Bongiorno, L. Di Piazza, D. Preiss:
A constructive minimal integral which includes Lebesgue integrable functions and derivatives. J. London Math. Soc. 62 (2000), 117–126.
DOI 10.1112/S0024610700008905 |
MR 1771855
[6] L. Di Piazza:
A Riemann-type minimal integral for the classical problem of primitives. Rend. Istit. Mat. Univ. Trieste 34 (2002 2003), 143–153.
MR 2013947
[7] R. A. Gordon:
The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Graduate Studies in Mathematics, AMS, 1994.
MR 1288751 |
Zbl 0807.26004
[8] Peng Yee Lee, R. Výborný:
The integral, An Easy Approach after Kurzweil and Henstock. Australian Mathematical Society Lecture Series 14, Cambridge University Press, 2000.
MR 1756319
[9] Š. Schwabik, M. Tvrdý, O. Vejvoda:
Differential and Integral Equations. Boundary Value Problems and Adjoints. D. Reidel Publishing Co., Dordrecht-Boston, Mass.-London, 1979.
MR 0542283