Variations of additive functions

Zoltán Buczolich; Washek Frank Pfeffer

Czechoslovak Mathematical Journal (1997)

  • Volume: 47, Issue: 3, page 525-555
  • ISSN: 0011-4642

Abstract

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We study the relationship between derivates and variational measures of additive functions defined on families of figures or bounded sets of finite perimeter. Our results, valid in all dimensions, include a generalization of Ward’s theorem, a necessary and sufficient condition for derivability, and full descriptive definitions of certain conditionally convergent integrals.

How to cite

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Buczolich, Zoltán, and Pfeffer, Washek Frank. "Variations of additive functions." Czechoslovak Mathematical Journal 47.3 (1997): 525-555. <http://eudml.org/doc/30382>.

@article{Buczolich1997,
abstract = {We study the relationship between derivates and variational measures of additive functions defined on families of figures or bounded sets of finite perimeter. Our results, valid in all dimensions, include a generalization of Ward’s theorem, a necessary and sufficient condition for derivability, and full descriptive definitions of certain conditionally convergent integrals.},
author = {Buczolich, Zoltán, Pfeffer, Washek Frank},
journal = {Czechoslovak Mathematical Journal},
keywords = {Riemann type integrals; additive functions; variational measures; derivatives; bounded sets of finite perimeter},
language = {eng},
number = {3},
pages = {525-555},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Variations of additive functions},
url = {http://eudml.org/doc/30382},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Buczolich, Zoltán
AU - Pfeffer, Washek Frank
TI - Variations of additive functions
JO - Czechoslovak Mathematical Journal
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 3
SP - 525
EP - 555
AB - We study the relationship between derivates and variational measures of additive functions defined on families of figures or bounded sets of finite perimeter. Our results, valid in all dimensions, include a generalization of Ward’s theorem, a necessary and sufficient condition for derivability, and full descriptive definitions of certain conditionally convergent integrals.
LA - eng
KW - Riemann type integrals; additive functions; variational measures; derivatives; bounded sets of finite perimeter
UR - http://eudml.org/doc/30382
ER -

References

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  10. 10.1512/iumj.1991.40.40011, Indiana Univ. Math. J. 40 (1991), 259–270. (1991) Zbl0747.26010MR1101229DOI10.1512/iumj.1991.40.40011
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  15. The spaces B V and quasilinear equations, Math. USSR-SB. 2 (1967), 255–267. (1967) MR0216338

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