Abstract
The notion of ergodicity of a measure-preserving transformation is generalized to finite sets of transformations. The main result is that if T 1, T 2, ..., T s are invertible commuting measure-preserving transformations of a probability space (X, ℬ, μ) then {Mathematical expression} for any f 1, f 2, ..., f s∈L x (X, ℬ, μ) iff T 1×T 2×...×T s and all the transformations T iTj 1, i≠j, are ergodic. The multiple recurrence theorem for a weakly mixing transformation follows as a special case.
Original language | English |
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Pages (from-to) | 307-314 |
Number of pages | 8 |
Journal | Israel Journal of Mathematics |
Volume | 49 |
Issue number | 4 |
DOIs | |
State | Published - 1 Dec 1984 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics (all)