A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals

C. K. Fong

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 3, page 531-536
  • ISSN: 0011-4642

Abstract

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We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.

How to cite

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Fong, C. K.. "A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals." Czechoslovak Mathematical Journal 52.3 (2002): 531-536. <http://eudml.org/doc/30721>.

@article{Fong2002,
abstract = {We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.},
author = {Fong, C. K.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Pettis integrability; HK-integrals; Saks-Henstock’s property; Pettis integrability; Henstock-Kurzweil integrals; Saks-Henstock property; Orlicz-Pettis theorem},
language = {eng},
number = {3},
pages = {531-536},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals},
url = {http://eudml.org/doc/30721},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Fong, C. K.
TI - A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 3
SP - 531
EP - 536
AB - We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.
LA - eng
KW - Pettis integrability; HK-integrals; Saks-Henstock’s property; Pettis integrability; Henstock-Kurzweil integrals; Saks-Henstock property; Orlicz-Pettis theorem
UR - http://eudml.org/doc/30721
ER -

References

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  1. 10.2307/2974874, Amer. Math. Monthly 103 (1996), 625–632. (1996) Zbl0884.26007MR1413583DOI10.2307/2974874
  2. Normed Linear Spaces, Academic Press Inc., New York, 1962. (1962) Zbl0100.10802MR0145316
  3. Sequences and Series in Banach Spaces, Springer-Verlag, New York, 1984. (1984) MR0737004
  4. Vector Measures. Mathematical Surveys, No.  15, Amer. Math. Soc., Providence, 1997. (1997) MR0453964
  5. The General Theory of Integration, Clarendon Press, Oxford, 1991. (1991) Zbl0745.26006MR1134656
  6. The Riemann Approach to Integration. Cambridge Tracts in Mathematics, No.  109, Cambridge University Press, Cambridge, 1993. (1993) MR1268404
  7. Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970. (1970) Zbl0207.13501MR0290095
  8. Abstract Bochner and McShane Integrals, Ann. Math. Sil. 1564(10) (1996), 21–56. (1996) Zbl0868.28005MR1399609

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