Ergodic decomposition of a stationary channel operator

Pointwise weak* topology is defined for the set of all channel operators and the latter is shown to be compact with this topology. Since the set of all ergodic stationary channel operators coincides with the set of all extreme points of the set of stationary channel operators, each stationary channel operator is represented as an integral of ergodic stationary channel operators with respect to a suitable probability measure on the set of all ergodic stationary channel operators.