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

A counterexample against the Lesche stability of a generic entropy functional