Absolute continuity theorems for abstract Riemann integration

E. de Amo; R. del Campo; M. Díaz Carillo

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 3, page 793-807
  • ISSN: 0011-4642

Abstract

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Absolute continuity for functionals is studied in the context of proper and abstract Riemann integration examining the relation to absolute continuity for finitely additive measures and giving results in both directions: integrals coming from measures and measures induced by integrals. To this end, we look for relations between the corresponding integrable functions of absolutely continuous integrals and we deal with the possibility of preserving absolute continuity when extending the elemental integrals.

How to cite

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Amo, E. de, Campo, R. del, and Díaz Carillo, M.. "Absolute continuity theorems for abstract Riemann integration." Czechoslovak Mathematical Journal 57.3 (2007): 793-807. <http://eudml.org/doc/31163>.

@article{Amo2007,
abstract = {Absolute continuity for functionals is studied in the context of proper and abstract Riemann integration examining the relation to absolute continuity for finitely additive measures and giving results in both directions: integrals coming from measures and measures induced by integrals. To this end, we look for relations between the corresponding integrable functions of absolutely continuous integrals and we deal with the possibility of preserving absolute continuity when extending the elemental integrals.},
author = {Amo, E. de, Campo, R. del, Díaz Carillo, M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {finitely additive integration; abstract Riemann integration; absolute continuity; finitely additive integration; abstract Riemann integration; absolute continuity},
language = {eng},
number = {3},
pages = {793-807},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Absolute continuity theorems for abstract Riemann integration},
url = {http://eudml.org/doc/31163},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Amo, E. de
AU - Campo, R. del
AU - Díaz Carillo, M.
TI - Absolute continuity theorems for abstract Riemann integration
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 793
EP - 807
AB - Absolute continuity for functionals is studied in the context of proper and abstract Riemann integration examining the relation to absolute continuity for finitely additive measures and giving results in both directions: integrals coming from measures and measures induced by integrals. To this end, we look for relations between the corresponding integrable functions of absolutely continuous integrals and we deal with the possibility of preserving absolute continuity when extending the elemental integrals.
LA - eng
KW - finitely additive integration; abstract Riemann integration; absolute continuity; finitely additive integration; abstract Riemann integration; absolute continuity
UR - http://eudml.org/doc/31163
ER -

References

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