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Correction: Entropy and the Consistent Estimation of Joint Distributions

Katalin Marton and Paul C. Shields
The Annals of Probability
Vol. 24, No. 1 (Jan., 1996), pp. 541-545
Stable URL: http://www.jstor.org/stable/2244857
Page Count: 5
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Correction: Entropy and the Consistent Estimation of Joint Distributions
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Abstract

Jeff Steif has brought to our attention an error on page 975 of our paper. Our argument that inequality (30) implies the immediately following inequality has a gap. A closer look shows an even more serious problem, namely, Lemma 6 as stated is probably not true, since nothing in the weak Bernoulli property precludes the possibility that splitting sets for xn 1 may depend on past coordinates {xi:i ≤ 0}. With a modified definition of the splitting concept an alternative version of Lemma 6 is true and this is sufficient to prove our principal theorem, Theorem 4. The following text replaces the discussion from the paragraph preceding Lemma 5 on page 973 to the end of Section 3 on page 976.

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