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Mixtures of nonatomic measures

Authors: K. P. S. Bhaskara Rao and M. Bhaskara Rao
Journal: Proc. Amer. Math. Soc. 33 (1972), 507-510
MSC: Primary 28A40; Secondary 28A35
MathSciNet review: 0293048
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Abstract: In this paper, we answer the following question: Is a mixture of nonatomic measures nonatomic? The answer turns out to be no, in general. Four sufficient conditions are given under which mixtures become nonatomic.

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

  • [1] R. A. Johnson, Atomic and nonatomic measures, Proc. Amer. Math. Soc. 25 (1970), 650-655. MR 0279266 (43:4989)
  • [2] J. Neveu, Bases mathématiques du calcul des probabilités, Masson, Paris, 1964; English transl., Holden-Day, San Francisco, Calif., 1965. MR 33 #6659; MR 33 #6660. MR 0198504 (33:6659)

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Keywords: Atom of a $ \sigma $-algebra, atom of a measure, nonatomic measure, transition probability, mixture, separable and Lindelöf topological spaces
Article copyright: © Copyright 1972 American Mathematical Society

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