A concept of absolute continuity and a Riemann type integral
Bongiorno, B. ; Pfeffer, Washek Frank
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 189-196 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1992-01-01
Classification:  26A39,  26B15,  26B30
@article{118488,
     author = {B. Bongiorno and Washek Frank Pfeffer},
     title = {A concept of absolute continuity and a Riemann type integral},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {189-196},
     zbl = {0776.26011},
     mrnumber = {1189651},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118488}
}
Bongiorno, B.; Pfeffer, Washek Frank. A concept of absolute continuity and a Riemann type integral. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 189-196. http://gdmltest.u-ga.fr/item/118488/

Bongiorno B.; Giertz M.; Pfeffer W.F. Some nonabsolutely convergent integrals in the real line, to appear. | MR 1171108 | Zbl 0774.26003

Federer H. Geometric Measure Theory, Springer-Verlag New York (1969). (1969) | MR 0257325 | Zbl 0176.00801

Gordon R. A descriptive characterization of the generalized Riemann integral, Real Analysis Exchange 15:1 (1989-1990), 397-400. (1989-1990) | MR 1042557 | Zbl 0703.26009

Massari U.; Miranda M. Minimal Surfaces in Codimension One, North-Holland Amsterdam (1984). (1984) | MR 0795963

Pfeffer W.F. An integral in geometric measure theory, to appear. | MR 1225672 | Zbl 0797.26007

Pfeffer W.F. A Riemann type definition of a variational integral, Proc. American Math. Soc. 114 (1992), 99-106. (1992) | MR 1072090 | Zbl 0749.26006

Pfeffer W.F. A descriptive definition of a variational integral and applications, Indiana Univ. J. 40 (1991), 259-270. (1991) | MR 1101229 | Zbl 0747.26010

Pfeffer W.F. The Gauss-Green theorem, Adv. Math. 87 (1991), 93-147. (1991) | MR 1102966 | Zbl 0732.26013

Saks S. Theory of the Integral, Dover New York (1964). (1964) | MR 0167578

Volpert A.I. The spaces $BV$ and quasilinear equations, Mathematics USSR-Sbornik 2 (1967), 225-267. (1967) | MR 0216338