  We describe analytical properties of the average output entropy of a quantum
channel as a function of a pair (channel, input ensemble). In particular, tight
semicontinuity bounds for this function with the rank/energy constraints are
obtained by using the modified semicontinuity bounds for the quantum
conditional entropy of quantum-classical states and a special approximation
technique.
  Several applications are considered. New semicontinuity and continuity bounds
for the output Holevo information of a channel as a function of a pair
(channel, input ensemble) are obtained. The semicontinuity bound for the
entanglement of formation with the rank constraint obtained in [1] is improved.
  In the preliminary part, some results concerning ensembles of quantum states
are presented. In particular, a new useful metric on the set of generalized
ensembles is proposed and explored. The concept of passive energy of an
ensemble introduced here plays an important role in the article.
