科研之友
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摘要
We provide a counterexample to show that the generic form of entropy S(p) = Sigma(i) g(p(i)), is not always stable against small variation of probability distribution (Lesche stability) even if g is concave function on [0, 1] and of class C(2) 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.
