Does, under iteration, all strongly mixing transformations tend to spread sets out, not only in (ordinary) diameter, but also in harmonic diameter?

Question

In [R. E. Rice, On mixing transformations, Aequationes Math. 17 (1978), 104 – 108; Theorem 2 (motivated by some physical phenomena and offer some clarifications of these phenomena)] it is shown that, under iteration, all (strongly) mixing transformations tend to spread sets out in (ordinary) diameter. Thus, even though some set A may not spread out in “volume” (measure), there is a very definite sense in which A does not remain small. Even though a large set cannot have a small diameter and a set with a large diameter cannot be truly small, it is still true that the diameter of a set need not be a good measure of its size and shape. A better measure is furnished by the harmonic diameter, (geometric) transfinite diameter and the generalized diameters.