Geodesic
A concept of absolute continuity and a Riemann type integral
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 189-196 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 26A39, 26B15, 26B30
Keywords: sets of bounded variation; partitions; gages; generalized absolute continuity 
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Bongiorno, B.; Pfeffer, W. F. A concept of absolute continuity and a Riemann type integral. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 189-196. http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a0/

[B-Gi-P] Bongiorno B., Giertz M., Pfeffer W.F.: Some nonabsolutely convergent integrals in the real line. to appear. | MR | Zbl

[Fe] Federer H.: Geometric Measure Theory. Springer-Verlag New York (1969). | MR | Zbl

[Go] Gordon R.: A descriptive characterization of the generalized Riemann integral. Real Analysis Exchange 15:1 (1989-1990), 397-400. | MR | Zbl

[M-M] Massari U., Miranda M.: Minimal Surfaces in Codimension One. North-Holland Amsterdam (1984). | MR

[PP1] Pfeffer W.F.: An integral in geometric measure theory. to appear. | MR | Zbl

[PP2] Pfeffer W.F.: A Riemann type definition of a variational integral. Proc. American Math. Soc. 114 (1992), 99-106. | MR | Zbl

[PP3] Pfeffer W.F.: A descriptive definition of a variational integral and applications. Indiana Univ. J. 40 (1991), 259-270. | MR | Zbl

[PP4] Pfeffer W.F.: The Gauss-Green theorem. Adv. Math. 87 (1991), 93-147. | MR | Zbl

[S] Saks S.: Theory of the Integral. Dover New York (1964). | MR

[V] Volpert A.I.: The spaces $BV$ and quasilinear equations. Mathematics USSR-Sbornik 2 (1967), 225-267. | MR