  The necessary conditions (NC) that reconcile canonical probability
distributions obtained from the q-maximum entropy principle, subjected to both
i) the additive duality of generalized statistics and ii) normal averages
expectations with the large deviation theory, are derived. The validity of
these necessary conditions is established on the basis of a result concerning
large deviation properties of conditional measures. The NC for normal averages
expectations are advantageous because they avoid the excessively prohibitive
conditions obtained by previous studies when employing other forms for defining
q-expectations. Numerical examples for an exemplary case are provided.
