 for all subsets \(A\) and \(B\) of \(X\). The vertical strokes denote the so-called absolute value; for instance: \(\lvert 5 \rvert = \lvert -5 \rvert = 5\). One can prove that there is a strict implication relation between the three dynamical properties we have introduced so far: strong mixing implies weak mixing, but not vice versa; and weak mixing implies ergodicity, but not vice versa. Hence, strong mixing is stronger condition than weak mixing, and weak mixing is stronger condition than ergodicity.