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E. Bishop, R. Phelps (1986)
THE SUPPORT FUNCTIONALS OF A CONVEX SET
Patrick Billingsley (1966)
Ergodic theory and information
P. Walters (1975)
A VARIATIONAL PRINCIPLE FOR THE PRESSURE OF CONTINUOUS TRANSFORMATIONS.American Journal of Mathematics, 97
M Brin, G Stuck (2002)
Introduction to Dynamical Systems
R. Bowen (1975)
Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms
D. Ruelle (1978)
Thermodynamic Formalism: The Mathematical Structures of Classical Equilibrium Statistical Mechanics
(2002)
Introduction to Dynamical Systems, Cambridge: Cambridge Univ
The limit frequency properties of trajectories of the simplest dynamical system generated by the left shift on the space of sequences of letters from a finite alphabet are studied. The following modification of the Shannon-McMillan-Breiman theorem is proved: for any invariant (not necessarily ergodic) probability measure μ on the sequence space, the logarithm of the cardinality of the set of all μ-typical sequences of length n is equivalent to nh(μ), where h(μ) is the entropy of the measure μ. Here a typical finite sequence of letters is understood as a sequence such that the empirical measure generated by it is close to μ (in the weak topology).
Differential Equations – Springer Journals
Published: Apr 24, 2019
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