Simultaneous hitting characterization of weak mixing
= Simultaneous hitting characterization of weak mixing
A system is weakly mixing exactly when, for every positive-measure $A,B,C$, some $n\geq1$ makes both $T^{-n}A\cap B$ and $T^{-n}A\cap C$ have positive measure. This is the finite simultaneous-hitting form of the density-one correlation characterization.