  We prove that for any infinite-dimensional quantum channel the entropic
disturbance (defined as difference between the $\chi$-quantity of a generalized
ensemble and that of the image of the ensemble under the channel) is lower
semicontinuous on the natural set of its definition. We establish a number of
useful corollaries of this property, in particular, we prove the continuity of
the output $\chi\textrm{-}$quantity and the existence of $\chi$-optimal
ensemble for any quantum channel under the energy-type input constraint.
