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The proof is based on the “information functional” l(∫- ∞+ ∞ p(x)log p(x)dx + 1/2log D(x)) , $p(x)$ being the density of the random variable X. Some new dependencies between the Shannon and Fisher information quantities are established and an information theoretic interpretation of the Lindeberg condition is given.
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Ju. Linnik (1959) studied this question.
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