o vs. ℤ

Part of the Graduate Texts in Mathematics book series (GTM, volume 234)


The title of this chapter calls for an explanation: Given a base space X, an endomorphism σ of X, and a prescribed weight function W on X, we saw in Section 1.2 that there is an associated measure Px on the space of infinite paths rooted at x; see Figure 1.1 (p. 8) for an illustration. As noted, the function W determines the transition probabilities that go into the probability measure Px as follows: For two “successive” points y and z on such a path in X, a transition is possible if σ (z)=y, and the transition probability is then W (z). If points on the path are further apart, we use a natural formula for conditional probabilities.


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© Springer Science+Business Media, LLC 2006

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