Blocks, Measures and Bayesian Extensions

We restrict our attention for the moment to elementary one-dimensional systems, so that each cell of the lattice is indexed by an integer i G Z and takes on one jf two possible values, Oj S = 0,1. We recall from section 2.2,1 that the collection of all configurations, or the CA phase space, L 3 is a compact metric space under the metric 

Cylinders thus specify configurations with prescribed values at a finite number of cells. 

Each A-cylinder may be put into a one-to-one correspondence with an N-block, Bf4 given Bf, the corresponding cylinder set is defined by (3 ) = n G F = 

CA Action on Probability Measures To facilitate the mathematical description of the general action of on F, we introduce a probability measure p on F. The action of on block-subsets of F induces an action on measures on F of the following form [guto87a]  

We will, in particular, be interested in the invariant (or limit) measure, Poo ), of, defined as 

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