On integration of vector functions with respect to vector measures

José Rodríguez

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 3, page 805-825
  • ISSN: 0011-4642

Abstract

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We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff integral was first considered by Dobrakov under the name S * -integral. Our main result states that S * -integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function is measurable and McShane integrable if and only if it is Dobrakov integrable (i.e. Bartle *-integrable).

How to cite

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Rodríguez, José. "On integration of vector functions with respect to vector measures." Czechoslovak Mathematical Journal 56.3 (2006): 805-825. <http://eudml.org/doc/31069>.

@article{Rodríguez2006,
abstract = {We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff integral was first considered by Dobrakov under the name $S^\{*\}$-integral. Our main result states that $S^\{*\}$-integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function is measurable and McShane integrable if and only if it is Dobrakov integrable (i.e. Bartle *-integrable).},
author = {Rodríguez, José},
journal = {Czechoslovak Mathematical Journal},
keywords = {Bartle $^*$-integral; Dobrakov integral; McShane integral; Birkhoff integral; $S^*$-integral; Bartle -integral; Dobrakov integral; McShane integral; Birkhoff integral; -integral},
language = {eng},
number = {3},
pages = {805-825},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On integration of vector functions with respect to vector measures},
url = {http://eudml.org/doc/31069},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Rodríguez, José
TI - On integration of vector functions with respect to vector measures
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 805
EP - 825
AB - We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff integral was first considered by Dobrakov under the name $S^{*}$-integral. Our main result states that $S^{*}$-integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function is measurable and McShane integrable if and only if it is Dobrakov integrable (i.e. Bartle *-integrable).
LA - eng
KW - Bartle $^*$-integral; Dobrakov integral; McShane integral; Birkhoff integral; $S^*$-integral; Bartle -integral; Dobrakov integral; McShane integral; Birkhoff integral; -integral
UR - http://eudml.org/doc/31069
ER -

References

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