  The generalized entropic measure, which is optimized by a given arbitrary
distribution under the constraints on normalization of the distribution and the
finite ordinary expectation value of a physical random quantity, is considered
and its Lesche stability property (that is different from thermodynamic
stability) is examined. A general condition, under which the generalized
entropy becomes stable, is derived. Examples known in the literature, including
the entropy for the stretched-exponential distribution, the quantum-group
entropy, and the kappa-entropy are discussed.
