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A complete metric space of sub--algebras

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Part of the Lecture Notes in Mathematics book series (LNM,volume 296)

Abstract

In this paper it is shown that a metric can be defined on the set of all sub--algebras of a given -algebra. It is observed that C. Rajki's Theorem ([9]) on the metric space of discrete probability distributions turns out to be a particular case of our theorem which also provides a much shorter proof. The completeness and other properties of this metric space are also established.

Keywords

  • Equivalence Class
  • Probability Space
  • Ergodic Theory
  • Convergent Subsequence
  • Borel Subset

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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© 1973 Springer-Verlag

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Singh, J.M. (1973). A complete metric space of sub--algebras. In: Behara, M., Krickeberg, K., Wolfowitz, J. (eds) Probability and Information Theory II. Lecture Notes in Mathematics, vol 296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059824

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  • DOI: https://doi.org/10.1007/BFb0059824

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06211-0

  • Online ISBN: 978-3-540-38485-4

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