Is there an example of a non-trivial measure preserving transformation that is uniquely ergodic and strongly mixing (in the measure theoretic sense)? This was asked [here](https://math.stackexchange.com/questions/1126789/strongly-mixing-uniquely-ergodic-dynamical-system), but with no answer. 



Uniquely ergodic and strongly mixing transformation
The Jewett-Krieger Theorem states that every ergodic measure-preserving transformation of a standard probability space can be realised as a uniquely ergodic topological dynamical system on a compact metric space. If the metric entropy of the original system is strictly less than $\log d$, where $d$ is an integer, then additionally this topological dynamical system can be taken to be a closed shift-invariant subset of the full shift on $d$ symbols. A proof of this theorem can be found in the book *Ergodic theory on compact spaces* by Denker, Grillenberger and Sigmund.


A natural example of a uniquely ergodic mixing flow is the horocycle flow on a surface of constant negative curvature. Explicit examples of mixing uniquely ergodic maps have been constructed by Grillenberger in his paper *Constructions of strictly ergodic systems II*, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 25 (1972/73) 335-342.


