A free product formula for the sofic dimension
arXiv:1308.0663 · doi:10.4153/CJM-2014-019-5
Abstract
It is proved that if is free product of probability measure preserving -regular ergodic discrete groupoids amalgamated over an amenable subgroupoid , then the sofic dimension satisfies the equality \[ s(G)=\h(G_1^0)s(G_1)+\h(G_2^0)s(G_2)-\h(G_3^0)s(G_3) \] where $\h$ is the normalized Haar measure on .