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1. SOFIC DIMENSION FOR DISCRETE MEASURED GROUPOIDS.

Author

DYKEMA, KEN, KERR, DAVID, and PICHOT, MIKAËL

Subjects
DIMENSIONS, DISCRETE groups, MEASURE theory, GROUPOIDS, PROBABILITY measures, APPROXIMATION theory
Abstract

For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger and larger finite sets. In the case of groups we give a formula for free products with amalgamation over an amenable subgroup. We also prove a free product formula for measurepreserving actions. [ABSTRACT FROM AUTHOR]

Published
2014
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