Rank, rigidity of factors, and weak closure of measure-preserving \(\mathbb Z^n\)-actions

DOI10.3103/S0027132208040025zbMath1304.37005MaRDI QIDQ2512991

V. V. Ryzhikov

Publication date: 2 February 2015

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

Mathematics Subject Classification ID

General groups of measure-preserving transformations (28D15) General groups of measure-preserving transformations and dynamical systems (37A15) Measurable group actions (22F10)

Cites Work

• A canonical structure theorem for finite joining-rank maps
• Conjugations, joinings, and direct products of locally rank one dynamical systems
• The commutant is the weak closure of the powers, for rank-1 transformations
• MIXING, RANK, AND MINIMAL SELF-JOINING OF ACTIONS WITH AN INVARIANT MEASURE
• Weak Closure Theorem fails for Z²-actions

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