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- W95973628 abstract "Abstract Let Ω = x ∞ 0 {0, 1, s-1}, s 2, and let T be the shift on Ω. Let P(Ω, T) be the compact convex set of all shift invariant normalized Borel measures on Ω, and let M(Ω, T) be the set of all Markov measures in P(Ω, T). Let M 1 (Ω, T) be the set of all Markov measures in M(Ω, T) that are induced by irreducible stochastic matrices, and let M 2 (Ω, T) be the set of all Markov measures in M(Ω, T) that are induced by reducible recurrent stochastic matrices. We show that both M(Ω, T) and M 2 (Ω, T) are compact, connected non-convex subsets of P(Ω, T), and M 1 (Ω, T) is an open, connected, strongly nonconvex dense subset of M(Ω, T) such that M(Ω, T) = M 1 (Ω, T) U M 2 (Ω, T). We also show that the entropy map of the shift is an affine upper semi continuous function from P(Ω, T) onto [0, log s] and is a continuous function on M(Ω, T) which maps M 1 (Ω, T) onto [0, log s]." @default.
- W95973628 created "2016-06-24" @default.
- W95973628 creator A5021229099 @default.
- W95973628 date "1988-01-01" @default.
- W95973628 modified "2023-09-27" @default.
- W95973628 title "Shift Invariant Markov Measures and the Entropy Map of the Shift" @default.
- W95973628 cites W2751862591 @default.
- W95973628 doi "https://doi.org/10.1016/s0304-0208(08)71332-x" @default.
- W95973628 hasPublicationYear "1988" @default.
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