Information Meaning of Entropy of Nonergodic Measures

Autor:	V. I. Bakhtin
Rok vydání:	2019
Předmět:	Pure mathematics Partial differential equation Logarithm General Mathematics Ordinary differential equation Ergodic theory Entropy (information theory) Empirical measure Analysis Probability measure Finite sequence Mathematics
Zdroj:	Differential Equations. 55:294-302
ISSN:	1608-3083 0012-2661
Popis:	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).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::40aa4fcb03d8166413f836762b9f0e47 https://doi.org/10.1134/s0012266119030029 Zobrazit plný text záznamu Plný text ve formátu PDF