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.
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References
R. G. Bartle: Return to the Riemann integral. Amer. Math. Monthly 103 (1996), 625–632.
M. M. Day: Normed Linear Spaces. Academic Press Inc., New York, 1962.
J. Diestel: Sequences and Series in Banach Spaces. Springer-Verlag, New York, 1984.
J. Diestel and J. J. Uhl, Jr.: Vector Measures. Mathematical Surveys, No. 15. Amer. Math. Soc., Providence, 1997.
R. Henstock: The General Theory of Integration. Clarendon Press, Oxford, 1991.
W. F. Pfeffer: The Riemann Approach to Integration. Cambridge Tracts in Mathematics, No. 109. Cambridge University Press, Cambridge, 1993.
E. M. Stein: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, 1970.
Š. Schwabik: Abstract Bochner and McShane Integrals. Ann. Math. Sil. 1564(10) (1996), 21–56.
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Fong, C.K. A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals. Czechoslovak Mathematical Journal 52, 531–536 (2002). https://doi.org/10.1023/A:1021719627933
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DOI: https://doi.org/10.1023/A:1021719627933