A note on the Denjoy integrability of abstractly-valued functions
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- by T. J. Morrison PDF
- Proc. Amer. Math. Soc. 61 (1976), 385-386 Request permission
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
- C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 115069, DOI 10.4064/sm-17-2-151-164
- 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
- Donald W. Solomon, Denjoy integration in abstract spaces, Memoirs of the American Mathematical Society, No. 85, American Mathematical Society, Providence, R.I., 1969. MR 0239045
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 385-386
- MSC: Primary 28A45; Secondary 26A39, 46G10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0486403-4
- MathSciNet review: 0486403