Quasifactors of ergodic systems with positive entropy | Zendy

Eli Glasner | Zendy; Benjamin Weiss | Zendy

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Quasifactors of ergodic systems with positive entropy

Author(s) -

Eli Glasner,

Benjamin Weiss

Publication year - 2003

Publication title -

israel journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.168

H-Index - 63

eISSN - 1565-8511

pISSN - 0021-2172

DOI - 10.1007/bf02787413

Subject(s) - ergodic theory , mathematics , entropy (arrow of time) , pure mathematics , stationary ergodic process , discrete mathematics , combinatorics , invariant measure , physics , quantum mechanics

The relation between the two notions quasifactors and joinings is inves- tigated and the notion of a joining quasifactor is introduced. We clarify the close connection between quasifactors and symmetric infinite selfjoinings which arises from de Finetti-Hewitt-Savage theorem. Unlike the zero entropy case where quasifactors seems to preserve some properties of their parent system, it is shown that any er- godic system of positive entropy admits all ergodic systems of positive entropy as quasifactors. A restricted version of this result is obtained for joining quasifactors.

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