Proceedings of the Japan Academy

The information theoretic proof of Kac's theorem

Yoshiaki Itoh

Full-text: Open access

Article information

Source
Proc. Japan Acad., Volume 46, Number 3 (1970), 283-286.

Dates
First available in Project Euclid: 20 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195520409

Digital Object Identifier
doi:10.3792/pja/1195520409

Mathematical Reviews number (MathSciNet)
MR0278824

Zentralblatt MATH identifier
0209.49804

Subjects
Primary: 94.20
Secondary: 62.00

Citation

Itoh, Yoshiaki. The information theoretic proof of Kac's theorem. Proc. Japan Acad. 46 (1970), no. 3, 283--286. doi:10.3792/pja/1195520409. https://projecteuclid.org/euclid.pja/1195520409


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References

  • [1] Kac, M. 1.: On a characterization of normal distribution. Amer. J. Math., 61 (1939).
  • [2] Linnik, YU. V. 1.: An information theoretic proof of the central limit theorem with the Lindeberg condition. Theory of Probability and its Applications, 4, 288-299 (1959).
  • [3] Mckean, H. P. 1.: Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas. Arch. Rational Mech. Anal., 21, 343-367 (1966).
  • [4] Polya, G. 1: Herleitung des Gauss'schen Gesetzes aus einer Funktionalgleichung. Math. Zeit., 18, 96-103 (1923).
  • [5] Shannon, C. 1.: A mathematical theory of communication. Bell Syst. Tech. J., 27, 379-423, 623-656 (1948).