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A Free Product Formula for the Sofic Dimension
Published online by Cambridge University Press: 20 November 2018
Abstract
It is proved that if $G\,=\,{{G}_{1}}\,{{*}_{{{G}_{3}}}}\,{{G}_{2}}$ is free product of probability measure preserving $s$–regular ergodic discrete groupoids amalgamated over an amenable subgroupoid ${{G}_{3}}$, then the sofic dimension $s(G)$ satisfies the equality
where $\mathfrak{h}$ is the normalized Haar measure on $G$.
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- Copyright © Canadian Mathematical Society 2015
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