On sofic groupoids and their full groups (Q1671204)

In this work, the author proves that an aperiodic probability measure preserving (pmp) groupoid is sofic if and only if its full groupoid is metrically sofic, and he answers a question of \textit{C. T. Conley} et al. [Ergodic Theory Dyn. Syst. 33, No. 2, 334--374 (2013; Zbl 1268.05104)]. The author also invites us to answer the following question due to Vladimir Pestov: is a pmp equivalence relation sofic if and only if its full group is sofic? We must also remember that in [Proc. Am. Math. Soc. 143, No. 5, 1943--1950 (2015; Zbl 1362.20035).], \textit{G. Elek} proves that if a pmp equivalence relation is sofic then its full group is sofic.