Abstract Riemann integrability and measurability

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

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 4, page 1123-1139
  • ISSN: 0011-4642

Abstract

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We prove that the spectral sets of any positive abstract Riemann integrable function are measurable but (at most) a countable amount of them. In addition, the integral of such a function can be computed as an improper classical Riemann integral of the measures of its spectral sets under some weak continuity conditions which in fact characterize the integral representation.

How to cite

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de Amo, E., del Campo, R., and Carrillo, M. Díaz. "Abstract Riemann integrability and measurability." Czechoslovak Mathematical Journal 59.4 (2009): 1123-1139. <http://eudml.org/doc/37983>.

@article{deAmo2009,
abstract = {We prove that the spectral sets of any positive abstract Riemann integrable function are measurable but (at most) a countable amount of them. In addition, the integral of such a function can be computed as an improper classical Riemann integral of the measures of its spectral sets under some weak continuity conditions which in fact characterize the integral representation.},
author = {de Amo, E., del Campo, R., Carrillo, M. Díaz},
journal = {Czechoslovak Mathematical Journal},
keywords = {finitely additive integration; localized convergence; integral representation; weak continuity conditions; horizontal integration; finitely additive integration; localized convergence; integral representation; weak continuity condition; horizontal integration},
language = {eng},
number = {4},
pages = {1123-1139},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Abstract Riemann integrability and measurability},
url = {http://eudml.org/doc/37983},
volume = {59},
year = {2009},
}

TY - JOUR
AU - de Amo, E.
AU - del Campo, R.
AU - Carrillo, M. Díaz
TI - Abstract Riemann integrability and measurability
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 1123
EP - 1139
AB - We prove that the spectral sets of any positive abstract Riemann integrable function are measurable but (at most) a countable amount of them. In addition, the integral of such a function can be computed as an improper classical Riemann integral of the measures of its spectral sets under some weak continuity conditions which in fact characterize the integral representation.
LA - eng
KW - finitely additive integration; localized convergence; integral representation; weak continuity conditions; horizontal integration; finitely additive integration; localized convergence; integral representation; weak continuity condition; horizontal integration
UR - http://eudml.org/doc/37983
ER -

References

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