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Proceedings of the American Mathematical Society
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 22 #5872. MR 0115069 (22:5872)
  • [2] E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ., vol. 31, rev. ed., Amer. Math. Soc., Providence, R. I., 1957. MR 19, 664. MR 0089373 (19:664d)
  • [3] D. W. Solomon, Denjoy integration in abstract spaces, Mem. Amer. Math. Soc. No. 85 (1969). MR 39 #404. MR 0239045 (39:404)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0486403-4
PII: S 0002-9939(1976)0486403-4
Article copyright: © Copyright 1976 American Mathematical Society