A full descriptive definition of the BV-integral

B. Bongiorno; Luisa Di Piazza; Washek Frank Pfeffer

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 3, page 461-469
  • ISSN: 0010-2628

Abstract

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We present a Cauchy test for the almost derivability of additive functions of bounded BV sets. The test yields a full descriptive definition of a coordinate free Riemann type integral.

How to cite

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Bongiorno, B., Di Piazza, Luisa, and Pfeffer, Washek Frank. "A full descriptive definition of the BV-integral." Commentationes Mathematicae Universitatis Carolinae 36.3 (1995): 461-469. <http://eudml.org/doc/247732>.

@article{Bongiorno1995,
abstract = {We present a Cauchy test for the almost derivability of additive functions of bounded BV sets. The test yields a full descriptive definition of a coordinate free Riemann type integral.},
author = {Bongiorno, B., Di Piazza, Luisa, Pfeffer, Washek Frank},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Perimeter; partition; gage; absolute continuity; bounded variation; descriptive integrals; variational integral; bounded Caccioppoli set; Gauss-Green theorem},
language = {eng},
number = {3},
pages = {461-469},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A full descriptive definition of the BV-integral},
url = {http://eudml.org/doc/247732},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Bongiorno, B.
AU - Di Piazza, Luisa
AU - Pfeffer, Washek Frank
TI - A full descriptive definition of the BV-integral
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 3
SP - 461
EP - 469
AB - We present a Cauchy test for the almost derivability of additive functions of bounded BV sets. The test yields a full descriptive definition of a coordinate free Riemann type integral.
LA - eng
KW - Perimeter; partition; gage; absolute continuity; bounded variation; descriptive integrals; variational integral; bounded Caccioppoli set; Gauss-Green theorem
UR - http://eudml.org/doc/247732
ER -

References

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  1. Bongiorno B., Differentiation of set functions, Rend. Circ. Mat. Palermo 26 37-51 (1977). (1977) Zbl0399.28003MR0524331
  2. Evans L.C., Gariepy R.F., Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992. Zbl0804.28001MR1158660
  3. Kurzweil J., Jarník J., Equi-integrability and controlled convergence of Perron-type integrable functions, Real Anal. Ex. 17 110-139 (1991:92). (1991:92) MR1147361
  4. Pfeffer W.F., A descriptive definition of a variational integral and applications, Indiana Univ. Math. J. 40 259-270 (1991). (1991) Zbl0747.26010MR1101229
  5. Pfeffer W.F., The Gauss-Green theorem, Adv. Math. 87 93-147 (1991). (1991) Zbl0732.26013MR1102966
  6. Pfeffer W.F., The Riemann Approach to Integration, Cambridge Univ. Press, Cambridge, 1993. Zbl1143.26005MR1268404
  7. Saks S., Theory of the Integral, Dover, New York, 1964. Zbl0017.30004MR0167578
  8. Volpert A.I., The spaces BV and quasilinear equations, Math. USSR-SB. 2 255-267 (1967). (1967) MR0216338

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