Measure
A subshift of finite type may be endowed with any one of several different measures, thus leading to a measure-preserving dynamical system. A common object of study is the Markov measure, which is an extension of a Markov chain to the topology of the shift.
A Markov chain is a pair (P,π) consisting of the transition matrix, an matrix for which all and
for all i. The stationary probability vector has all and has
- .
A Markov chain, as defined above, is said to be compatible with the shift of finite type if whenever . The Markov measure of a cylinder set may then be defined by
The Kolmogorov-Sinai entropy with relation to the Markov measure is
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