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== Measure theory ==
{{See also|Subshift of finite type}}
[[File:Blackwell_HMM_example.png|thumb|193x193px|The hidden part of a hidden Markov model, whose observable states is non-Markovian
Given a Markov transition matrix and an invariant distribution on the states, a probability measure can be imposed on the set of subshifts. For example, consider the Markov chain given on the left on the states <math>A, B_1, B_2</math>, with invariant distribution <math>\pi = (2/7, 4/7, 1/7)</math>. By ignoring the distinction between <math>B_1, B_2</math>, this space of subshifts is projected on <math>A, B_1, B_2</math> into another space of subshifts on <math>A, B</math>, and this projection also projects the probability measure down to a probability measure on the subshifts on <math>A, B</math>.
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