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Aczel additive algebraic entropy amount of information arbitrary constant assume average amount average code length Behara and Nath channel code alphabet code is uniquely code word assigned complete probability distribution complete probability polynomial conditional entropy Consequently continuous function continuous solutions defined discrete probability distributions distinct code characters easily seen ergodic theory experiment following theorem functional equation given Hence increasing function inequality information theory intuitively joint entropy Lemma Let us choose loge mathematical measure of information measures of entropy monotonic and continuous monotonically increasing n-sequence nonadditive entropies nonadditive measures obvious occurs parabolic entropy PF(p polynomial entropy polynomial of degree positive integers Proof Let properties random variable taking reduces Renyi entropy satisfies sequence of length Shannon entropy statistically independent strictly monotonic subadditive symmetric function taking the values transcendental entropies Trigonometric Entropies two-dimensional uniquely decipherable code xi,x2,...,xn with probabilities