The McShane, PU and Henstock integrals of Banach valued functions

Luisa Di Piazza; Valeria Marraffa

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 3, page 609-633
  • ISSN: 0011-4642

Abstract

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Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals of vector valued functions are characterized.

How to cite

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Di Piazza, Luisa, and Marraffa, Valeria. "The McShane, PU and Henstock integrals of Banach valued functions." Czechoslovak Mathematical Journal 52.3 (2002): 609-633. <http://eudml.org/doc/30729>.

@article{DiPiazza2002,
abstract = {Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals of vector valued functions are characterized.},
author = {Di Piazza, Luisa, Marraffa, Valeria},
journal = {Czechoslovak Mathematical Journal},
keywords = {Pettis; McShane; PU and Henstock integrals; variational integrals; multipliers; Pettis integral; McShane integral; PU integral; variational integrals; multipliers; Henstock integral},
language = {eng},
number = {3},
pages = {609-633},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The McShane, PU and Henstock integrals of Banach valued functions},
url = {http://eudml.org/doc/30729},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Di Piazza, Luisa
AU - Marraffa, Valeria
TI - The McShane, PU and Henstock integrals of Banach valued functions
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 3
SP - 609
EP - 633
AB - Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals of vector valued functions are characterized.
LA - eng
KW - Pettis; McShane; PU and Henstock integrals; variational integrals; multipliers; Pettis integral; McShane integral; PU integral; variational integrals; multipliers; Henstock integral
UR - http://eudml.org/doc/30729
ER -

References

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