  We provide a counterexample to show that the generic form of entropy
S(p)=sum_i g(p_i) is not always stable against small variation of probability
distribution (Lesche stability) even if is concave function on [0,1] and
analytic on ]0,1]. Our conclusion is that the stability of such a generic
functional needs more hypotheses on the property of the function g, or in other
words, the stability of entropy cannot be discussed at this formal stage.
