Variational principles for Feldman–Katok metric mean dimension

We introduce the notion of Feldman–Katok metric mean dimensions in this note. We show metric mean dimensions defined by different dynamical metrics of phase space coincide under the (weak) tame growth of covering numbers, and establish variational principles for Feldman–Katok metric mean dimensions in terms of FK Katok ϵ-entropy and FK local ϵ-entropy function.