Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

A Generalized Shannon-McMillan Theorem for the Action of an Amenable Group on a Probability Space

J. C. Kieffer
The Annals of Probability
Vol. 3, No. 6 (Dec., 1975), pp. 1031-1037
Stable URL: http://www.jstor.org/stable/2959209
Page Count: 7
  • Read Online (Free)
  • Download ($19.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
A Generalized Shannon-McMillan Theorem for the Action of an Amenable Group on a Probability Space
Preview not available

Abstract

A generalization of the Shannon-McMillan Theorem ($L^1$ version) is obtained for the action of an amenable group on a probability space, thereby settling a conjecture of Pickel and Stepin. Interesting properties of the limit function are derived. The entropy of an action of an amenable group is defined.

Page Thumbnails

  • Thumbnail: Page 
1031
    1031
  • Thumbnail: Page 
1032
    1032
  • Thumbnail: Page 
1033
    1033
  • Thumbnail: Page 
1034
    1034
  • Thumbnail: Page 
1035
    1035
  • Thumbnail: Page 
1036
    1036
  • Thumbnail: Page 
1037
    1037