In Friedman and King's book "Rank one lightly mixing" and in Wenyu Chen's paper "the notion of mixing and rank one examples", the authors recall the definition of a lightly mixing transformation T:
for all $A,B$ of positive measure, $\liminf_{n\to \infty} \mu(T^{-n}A\cap B)>0$.
They suggest an equivalent characterization where it suffices to take $A=B$:
for all $A$ of positive measure, $\liminf_{n\to \infty} \mu(T^{-n}A\cap A)>0$.
I couldn't find how this characterization can be equivalent to the definition. Does anyone have a clue?