An algebraic Z^d - action is rigid if any measurable isomorphism between it and another Z^d - action is forced to have certain algebraic properties.
I will define what it means for a subset of Z^d to to be intrinsically nonmixing for such an action. This is a topological property of the action. Then I will define what it means for a collection of measurable sets to be a complete family for a subset of Z^d and the action.
Finally we will see how these properties are related and how they relate to the rigidity properties of an algebraic Z^d - action.