Article
Keywords:
sets of bounded variation; partitions; gages; generalized absolute continuity
Summary:
We present a descriptive definition of a multidimensional generalized Riemann integral based on a concept of generalized absolute continuity for additive functions of sets of bounded variation.
References:
[B-Gi-P] Bongiorno B., Giertz M., Pfeffer W.F.:
Some nonabsolutely convergent integrals in the real line. to appear.
MR 1171108 |
Zbl 0774.26003
[Go] Gordon R.:
A descriptive characterization of the generalized Riemann integral. Real Analysis Exchange 15:1 (1989-1990), 397-400.
MR 1042557 |
Zbl 0703.26009
[M-M] Massari U., Miranda M.:
Minimal Surfaces in Codimension One. North-Holland Amsterdam (1984).
MR 0795963
[PP2] Pfeffer W.F.:
A Riemann type definition of a variational integral. Proc. American Math. Soc. 114 (1992), 99-106.
MR 1072090 |
Zbl 0749.26006
[PP3] Pfeffer W.F.:
A descriptive definition of a variational integral and applications. Indiana Univ. J. 40 (1991), 259-270.
MR 1101229 |
Zbl 0747.26010
[S] Saks S.:
Theory of the Integral. Dover New York (1964).
MR 0167578
[V] Volpert A.I.:
The spaces $BV$ and quasilinear equations. Mathematics USSR-Sbornik 2 (1967), 225-267.
MR 0216338