Voiculescu, Dan The analogues of entropy and of Fisher’s information measure in free probability theory. I. (English) Zbl 0781.60006 Commun. Math. Phys. 155, No. 1, 71-92 (1993). Summary: Analogues of the entropy and Fisher information measure for random variables in the context of free probability theory are introduced. Monotonicity properties and an analogue of the Cramér-Rao inequality are proved. Cited in 14 ReviewsCited in 121 Documents MSC: 60A99 Foundations of probability theory 94A17 Measures of information, entropy Keywords:Fisher information measure; monotonicity properties; Cramér-Rao inequality × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Akhiezer, N.I.: The classical moment problem (in Russian) Moscow, 1961 · Zbl 0124.06202 [2] Balian, R.: Random matrices and information theory. Nuovo Cimento,LVIIB, No. 1, 183–193 (1968) · Zbl 0209.21903 [3] Barron, A.R.: Entropy and the central limit theorem. Ann. 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