  Partially observable Markov decision processes (POMDPs) are standard models
for dynamic systems with probabilistic and nondeterministic behaviour in
uncertain environments. We prove that in POMDPs with long-run average
objective, the decision maker has approximately optimal strategies with finite
memory. This implies notably that approximating the long-run value is
recursively enumerable, as well as a weak continuity property of the value with
respect to the transition function.
