About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Bongiorno, B. ; Di Piazza, L. ; Pfeffer, W. F.
A full descriptive definition of the BV-integral. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 36 (1995), issue 3, pp. 461-469
MSC: 26A39, 26B30, 28A75 | MR 1364486 | Zbl 0842.26009
Keywords:
Perimeter; partition; gage; absolute continuity
Summary:
We present a Cauchy test for the almost derivability of additive functions of bounded BV sets. The test yields a full descriptive definition of a coordinate free Riemann type integral.
References:
[1] Bongiorno B.: Differentiation of set functions. Rend. Circ. Mat. Palermo 26 37-51 (1977). MR 0524331 | Zbl 0399.28003
[2] Evans L.C., Gariepy R.F.: Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton, 1992. MR 1158660 | Zbl 0804.28001
[3] Kurzweil J., Jarník J.: Equi-integrability and controlled convergence of Perron-type integrable functions. Real Anal. Ex. 17 110-139 (1991:92). MR 1147361
[4] Pfeffer W.F.: A descriptive definition of a variational integral and applications. Indiana Univ. Math. J. 40 259-270 (1991). MR 1101229 | Zbl 0747.26010
[5] Pfeffer W.F.: The Gauss-Green theorem. Adv. Math. 87 93-147 (1991). MR 1102966 | Zbl 0732.26013
[6] Pfeffer W.F.: The Riemann Approach to Integration. Cambridge Univ. Press, Cambridge, 1993. MR 1268404 | Zbl 1143.26005
[7] Saks S.: Theory of the Integral. Dover, New York, 1964. MR 0167578 | Zbl 0017.30004
[8] Volpert A.I.: The spaces BV and quasilinear equations. Math. USSR-SB. 2 255-267 (1967). MR 0216338
Partner of
EuDML logo