Around King's Rank-One theorems: Flows and Z^n-actions

Details Around King's Rank-One theorems: Flows and Z^n-actions Around King's Rank-One theorems: Flows and Z^n-actions

2011-08-13

arxiv.org/abs/1108.2767v3

Mathematics

Probability

Scientific paper

We study the generalizations of Jonathan King's rank-one theorems (Weak-Closure Theorem and rigidity of factors) to the case of rank-one R-actions (flows) and rank-one Z^n-actions. We prove that these results remain valid in the case of rank-one flows. In the case of rank-one Z^n actions, where counterexamples have already been given, we prove partial Weak-Closure Theorem and partial rigidity of factors.

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