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January 1996 Correction: "Entropy and the consistent estimation of joint distributions"
Katalin Marton, Paul C. Shields
Ann. Probab. 24(1): 541-545 (January 1996).

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 $x{^n_1}$may depend on past coordinates $\{x_i:i \leq 0\}$. 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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Katalin Marton. Paul C. Shields. "Correction: "Entropy and the consistent estimation of joint distributions"." Ann. Probab. 24 (1) 541 - 545, January 1996.

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Published: January 1996
First available in Project Euclid: 16 January 2003

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 1 • January 1996
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