Weak mixing

Summary

A measure-preserving transformation is weakly mixing when the correlations $\mu(T^{-n}A \cap B) - \mu(A)\mu(B)$ tend to $0$ on average over $n$, in absolute value. It sits strictly between mixing and ergodicity. Weak mixing has a clean spectral meaning: the Koopman operator has no eigenfunctions other than the constants. It describes a system with no rotation hidden inside it.