Correction: "Entropy and the consistent estimation of joint distributions"

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.