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Additive and non-additive entropies of finite measurable partitions

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Probability and Information Theory II

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

Abstract

A geometrical representation of entropy leads to a generalization which, in special cases, reduces to the Shannon entropy and may easily be connected to the Rényi entropy. This, in two dimensions, is here called Parabolic entropy (which may further be generalized to higher dimensions). Parabolic entropy happens to be a particular case of Polynomial entropies of finite measurable partitions. Finally, some conditional entropies are defined and their properties have been studied in order to prepare a background for the study of entropy of endomorphisms etc. in ergodic theory and for proving Shannon-Wolfowitz coding theorem.

This research work was supported by the NRC (Canada) grant No. A2977.

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References

  1. Aczél, J. (1966), Lectures on Functional equations and their applications, Academic Press, New York.

    MATH  Google Scholar 

  2. Arnold, V. I. and Avez, A., (1968), Ergodic Problems of Classical Mechanics, W. A. Benjamin, Inc., New York.

    MATH  Google Scholar 

  3. Behara, M. (1968), "Entropy as a Measure of Utility in Decision Theory. Invited paper presented at Mathematisches Institut, Oberwolfach, W. Germany.

    Google Scholar 

  4. Billingsley, P. (1965), Ergodic Theory and Information, John Wiley and Sons, Inc., New York.

    MATH  Google Scholar 

  5. Brown, T. A. (1963), Entropy and Conjugacy, Ann. Math. Stat., 34, 226–232.

    Article  MathSciNet  MATH  Google Scholar 

  6. Chaundy, T. W.; Mcleod, J. B. (1960). "On a Functional equation", Proc. Edin. Math. Soc. Notes, 43 7–8.

    Article  MathSciNet  MATH  Google Scholar 

  7. Hardy, G. H.; Littlewood, J. E.; Polya, G. (1952), Inequalities, London, Cambridge Univ. Press.

    MATH  Google Scholar 

  8. Meshalkin, L. D. (1959), "A case of isomorphism of Bernoulli schemes", Dokl. Akad. Nauk. SSSR, 128, 41–44

    MathSciNet  Google Scholar 

  9. Renyi, A. (1961) "On Measures of Entropy and Information", Proc. Fourth Berk. Symp. on Math. Stat. and Prob. 1, 547–561.

    MathSciNet  MATH  Google Scholar 

  10. Renyi, A. (1960), "Az informacióelmélét Nehány alepvető kerdése", A Mag. Tud. Akad. III (Mat. es Fiz), Ostal. kozl. 257–282.

    Google Scholar 

  11. Shannon, C. E. (1948), "A Mathematical theory of communication", Bell Sys. Tech. Jour., 27; 379–423, 623–656.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. McMaster University, USA

    M. Behara & P. Nath

Authors
  1. M. Behara
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  2. P. Nath
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Editor information

M. Behara K. Krickeberg J. Wolfowitz

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© 1973 Springer-Verlag

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Behara, M., Nath, P. (1973). Additive and non-additive entropies of finite measurable partitions. 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/BFb0059821

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  • DOI: https://doi.org/10.1007/BFb0059821

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06211-0

  • Online ISBN: 978-3-540-38485-4

  • eBook Packages: Springer Book Archive

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