Corrections and Clarifications

The ergodic theory of discrete sample paths


Corrections as of July 22, 1996.

TeX syntax is used for mathematics, e. g., "a_b" means "a subscript b", and "a^b" means "a superscript b".

1. Page 162, 2nd line of Case 2: $T^i\in F$ should be $T^ix\in F$.

2. Page 187, paragraph 3, end of line 6: "the almost" should be "almost"

3. Page 236, Lemma IV.3.3 display and proof should be:

$$ 2^{-\alpha n} \mu(x_1^n)\leq\mu(x_1^n|x_{-\infty}^0 )\leq 2^{\a$ n}\mu(x_1^n). $$

\noindent{\em Proof.} By the ergodic theorem, $-(1/n)\log \mu(x_1^n|x_{-\infty}^0 )\rightarrow H$, almost surely, while, by the entropy theorem, $-(1/n) \log \mu(x_1^n )\rightarrow H$, almost surely. These two facts together imply the lemma.

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