Note on continuity of information rate (Q1203577)

The continuity property of the information rate is studied for finite alphabet communication processes. In three topologies of the input probability measures (``set-wise'' convergence, ``cylinder-wise'' convergence, Ornstein's \(\bar d\) distance). In particular, it is shown that for finite-memory stationary channels the information rate is continuous in the Ornstein \(\bar d\) distance.