2 problems

Let $(X,\mu,T)$ be an ergodic system satisfying the spectral hypothesis of Corollary, and let $(Y,\nu,S)$ be an ergodic nilsystem. A joining of these systems is a joining of the me…

Let $(X,T)$ be a minimal topological dynamical system, and let ${\rm Ind}_{fip}(X,T)$ denote its set of finite-independent pairs. Write $\Delta_X=\{(x,x):x\in X\}$. Unique ergodici…