On variable length coding of asymptotically mean stationary measures

We discuss variable length coding of doubly infinite sequences. The attention is paid to the problem how the coding affects probability measures defined for the sequences. Particularly studied is the class of asymptotically mean stationary (AMS) measures, which is closed under the investigated coding. We discuss explicit formulae for the stationary means and conditions for: preserving stationarity, equivalence of shift invariant $\sigma$-fields, preserving finite energy property, and equality of mutual information.