A loosely Bernoulli counterexample machine (Q1806721)

The author adapts \textit{D. S. Ornstein}'s rank one mixing construction [Proceedings of the Sixth Berkeley Symposium on Mathematical Statistical Probability, University of California 1970, Vol. II, 347-356 (1972; Zbl 0262.28009)], to construct a rank one mixing transformation \(T\) for which \(T\times T\times \dots\times T\) is loosely Bernoulli. Previous such examples were weakly mixing but not mixing. This answers a question of \textit{D. S. Ornstein, D. J. Rudolph} and \textit{B. Weiss} [Mem. Am. Math. Soc. 262 (1982; Zbl 0504.28019)].