International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 28, Pages 1755-1770

Ergodicity and extremality of AMS sources and channels

Yûichirô Kakihara

Department of Mathematics, California State University, San Bernardino 92407-2397, CA, USA

Received 3 March 2001; Revised 5 September 2001

Copyright © 2003 Yûichirô Kakihara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Asymptotically mean stationary (AMS) sources (probability measures) and channels are considered as an extension of stationary sources and channels. It is shown that each extreme point of the set of all AMS sources is ergodic, but not vice versa, and that each extreme point in the set of all AMS channels is ergodic, but not vice versa.