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Proceedings of the American Mathematical Society

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The range of a vector-valued measure


Author: Kurt Helmes
Journal: Proc. Amer. Math. Soc. 45 (1974), 309-310
MSC: Primary 28A45
DOI: https://doi.org/10.1090/S0002-9939-1974-0352396-1
MathSciNet review: 0352396
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Abstract: A short proof is given that the weak closure of the range of a totally nonatomic vector-valued measure is convex.


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

  • [1] J. F. C. Kingman and A. P. Robertson, On a theorem of Lyapunov, J. London Math. Soc. 43 (1968), 347-351. MR 37 #367. MR 0224768 (37:367)
  • [2] A. P. Robertson and W. J. Robertson, Topologische Vektorräume, B. I. Hochschultaschenbücher, Band 164/164a, Bibliographisches Institut, Mannheim, 1967. MR 35 #821.
  • [3] I. Tweddle, The range of a vector-valued measure, Glasgow Math. J. 13 (1972). MR 0310189 (46:9291)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0352396-1
Keywords: Vector measures, totally nonatomic
Article copyright: © Copyright 1974 American Mathematical Society

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