While point (3) is fairly standard and uses shadowing and closing properties of the shift, the other two are more subtle. Take any sequence of distinct elements of X, then extract a converging subsequence xi \to x \in X. This paper extends those of Glendinning and Sidorov and of Hare and Sidorov from the case of the doubling map to the more general β ? \beta italic_β-transformation. This paper extends those of Glendinning and Sidorov 3 and of Hare and Sidorov 6 from the case of the doubling map to the more general -transformation. measure, (2) every sequence of periodic measures has an accumulation point (in the topology of convergence on cylinders) which is a countably additive measure and (3) the set of periodic measures is weak dense in Mp,q. 1 Answer Sorted by: 1 Yes, in every infinite subshift X one finds a non-periodic element.
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