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Entropy and the central limit theorem. (English) Zbl 0599.60024
The author establishes a strengthened central limit theorem for densities showing monotone convergence in the sense of relative entropy. The relative entropy is defined by \[ D_ n=\int f(x) \log f(x)/\phi (x)dx \] where f is the density function of a random variable, X, with finite variance and \(\phi\) is the normal density with the same mean and variance as f.
Reviewer: L.Pardo

MSC:
60F05 Central limit and other weak theorems
94A17 Measures of information, entropy
62B10 Statistical aspects of information-theoretic topics
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