Previous |  Up |  Next


sets of bounded variation; partitions; gages; generalized absolute continuity
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.
[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
[Fe] Federer H.: Geometric Measure Theory. Springer-Verlag New York (1969). MR 0257325 | Zbl 0176.00801
[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
[PP1] Pfeffer W.F.: An integral in geometric measure theory. to appear. MR 1225672 | Zbl 0797.26007
[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
[PP4] Pfeffer W.F.: The Gauss-Green theorem. Adv. Math. 87 (1991), 93-147. MR 1102966 | Zbl 0732.26013
[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
Partner of
EuDML logo