Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on the Denjoy integrability of abstractly-valued functions


Author: T. J. Morrison
Journal: Proc. Amer. Math. Soc. 61 (1976), 385-386
MSC: Primary 28A45; Secondary 26A39, 46G10
MathSciNet review: 0486403
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Abstract: We present necessary and sufficient conditions on a Banach space $ X$ that the classes of strongly measurable $ X$-valued Denjoy-Pettis integrable and Denjoy-Gelfand integrable functions coincide.


References [Enhancements On Off] (What's this?)

  • [1] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 0115069
  • [2] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373
  • [3] Donald W. Solomon, Denjoy integration in abstract spaces, Memoris of the American Mathematical Society, No. 85, American Mathematical Society, Providence, R.I., 1969. MR 0239045

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0486403-4
Article copyright: © Copyright 1976 American Mathematical Society