Combinatorial independence in measurable dynamics

Details Combinatorial independence in measurable dynamics Combinatorial independence in measurable dynamics

2007-05-23

arxiv.org/abs/0705.3424v1

Mathematics

Dynamical Systems

44 pages

Scientific paper

We develop a fine-scale local analysis of measure entropy and measure sequence entropy based on combinatorial independence. The concepts of measure IE-tuples and measure IN-tuples are introduced and studied in analogy with their counterparts in topological dynamics. Local characterizations of the Pinsker von Neumann algebra and its sequence entropy analogue are given in terms of combinatorial independence, l_1 geometry, and Voiculescu's completely positive approximation entropy. Among the novel features of our local study is the treatment of general discrete acting groups, with the structural assumption of amenability in the case of entropy.

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