  This paper studies the optimization of observation channels (stochastic
kernels) in partially observed stochastic control problems. In particular,
existence and continuity properties are investigated mostly (but not
exclusively) concentrating on the single-stage case. Continuity properties of
the optimal cost in channels are explored under total variation, setwise
convergence, and weak convergence. Sufficient conditions for compactness of a
class of channels under total variation and setwise convergence are presented
and applications to quantization are explored.
