Mixing (mathematics) - Generalizations

Generalizations

The definition given above is sometimes called strong 2-mixing, to distinguish it from higher orders of mixing. A strong 3-mixing system may be defined as a system for which

holds for all measurable sets A, B, C. We can define strong k-mixing similarly. A system which is strong k-mixing for all k=2,3,4,... is called mixing of all orders.

It is unknown whether strong 2-mixing implies strong 3-mixing. It is known that strong m-mixing implies ergodicity.