Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-06T07:11:51.552Z Has data issue: false hasContentIssue false
  • English
  • Français

An Elementary Proof of Abramov’s Result on the Entropy of a Flow1)

Published online by Cambridge University Press:  22 January 2016

Shunji Ito
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let T be an automorphism on a probability space (Ω, B, P). Given a finite partition α of Ω, into disjoint measurable sets A1, A2, · · ·, An, its entropy is

(D.1)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 41 , February 1971 , pp. 1 - 5
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

Footnotes

1)

This paper is chiefly due to Pinsker’s work [1].

References

[1] Pinsker, M.S., Information and information stable of random variables and processes, Academy of Science SSSR, 1960.Google Scholar
[2] Abramov, L.M., On the entropy of a flow, Dok. Akad. Nauk. SSSR. Vol. 128 (1959) 873–875.Google Scholar
[3] Halmos, P.R., Entropy in ergodic theory Univ. of Chicago lecture notes, 1959.Google Scholar
[4] Maruyama, G., Transformations of flow, J. Math. Soc. Japan Vol. 18 (1966) 303–330.Google Scholar