Compactification of the Stationary Channel Space

✍ Scribed by Shigeo Akashi

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 94 KB
• Volume: 250
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2000.7108

✦ Synopsis

Topologization of the set consisting of all channels is given. This result is applied to the proof that the entropy rates and the transmission rate are jointly upper semi-continuous on the product topological space constructed from the stationary regular Borel probability measures and the stationary channels. Finally, it is proved that there exists a combination of an input stationary measure and a stationary channel having finite memory which can make the transmission rate maximal.