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.
Citation
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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