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

Entropy Zero $\times$ Bernoulli Processes are Closed in the $\bar d$-Metric

Paul Shields and J.-P. Thouvenot
The Annals of Probability
Vol. 3, No. 4 (Aug., 1975), pp. 732-736
Stable URL: http://www.jstor.org/stable/2959337
Page Count: 5
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Entropy Zero $\times$ Bernoulli Processes are Closed in the $\bar d$-Metric
Preview not available

Abstract

An entropy zero $\times$ Bernoulli process is a stationary finite state process whose shift transformation is the direct product of an entropy zero transformation and a Bernoulli shift. We show that the class of such transformations which are ergodic is closed in the $\bar{d}$-metric. The $\bar{d}$-metric measures how closely two processes can be joined to form a third stationary process.

Page Thumbnails

  • Thumbnail: Page 
732
    732
  • Thumbnail: Page 
733
    733
  • Thumbnail: Page 
734
    734
  • Thumbnail: Page 
735
    735
  • Thumbnail: Page 
736
    736