A concept of absolute continuity and a Riemann type integral

B. Bongiorno; Washek Frank Pfeffer

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 2, page 189-196
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Bongiorno, B., and Pfeffer, Washek Frank. "A concept of absolute continuity and a Riemann type integral." Commentationes Mathematicae Universitatis Carolinae 33.2 (1992): 189-196. <http://eudml.org/doc/247366>.

@article{Bongiorno1992,
abstract = {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.},
author = {Bongiorno, B., Pfeffer, Washek Frank},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sets of bounded variation; partitions; gages; generalized absolute continuity; Kurzweil-Henstock integrals; multidimensional Riemann type integral; absolute continuity; additive functions},
language = {eng},
number = {2},
pages = {189-196},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A concept of absolute continuity and a Riemann type integral},
url = {http://eudml.org/doc/247366},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Bongiorno, B.
AU - Pfeffer, Washek Frank
TI - A concept of absolute continuity and a Riemann type integral
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 2
SP - 189
EP - 196
AB - 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.
LA - eng
KW - sets of bounded variation; partitions; gages; generalized absolute continuity; Kurzweil-Henstock integrals; multidimensional Riemann type integral; absolute continuity; additive functions
UR - http://eudml.org/doc/247366
ER -

References

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  1. Bongiorno B., Giertz M., Pfeffer W.F., Some nonabsolutely convergent integrals in the real line, to appear. Zbl0774.26003MR1171108
  2. Federer H., Geometric Measure Theory, Springer-Verlag New York (1969). (1969) Zbl0176.00801MR0257325
  3. Gordon R., A descriptive characterization of the generalized Riemann integral, Real Analysis Exchange 15:1 (1989-1990), 397-400. (1989-1990) Zbl0703.26009MR1042557
  4. Massari U., Miranda M., Minimal Surfaces in Codimension One, North-Holland Amsterdam (1984). (1984) MR0795963
  5. Pfeffer W.F., An integral in geometric measure theory, to appear. Zbl0797.26007MR1225672
  6. Pfeffer W.F., A Riemann type definition of a variational integral, Proc. American Math. Soc. 114 (1992), 99-106. (1992) Zbl0749.26006MR1072090
  7. Pfeffer W.F., A descriptive definition of a variational integral and applications, Indiana Univ. J. 40 (1991), 259-270. (1991) Zbl0747.26010MR1101229
  8. Pfeffer W.F., The Gauss-Green theorem, Adv. Math. 87 (1991), 93-147. (1991) Zbl0732.26013MR1102966
  9. Saks S., Theory of the Integral, Dover New York (1964). (1964) MR0167578
  10. Volpert A.I., The spaces B V and quasilinear equations, Mathematics USSR-Sbornik 2 (1967), 225-267. (1967) MR0216338

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