ABSTRACT
This chapter contains a review of the basic concepts of invariant sets and functions, of invariant measures viewed as a relationship between a set of transformations and a σfield, of ergodicity, mixing, and of the existence of invariant measures. The point properties of invariance are carefully displayed in order to obtain a basis for an operational version of those abstract concepts. It is also shown that almost sure invariance does require particular attention insofar as the almost sure invariant σ-field is, in general, different from the completed invariant σfield. The chapter draws upon and considerably extends Florens. In particular, results on the admissibility of reductions through invariance, characterization of a.s. invariant σfields, and randomization of transformations have been developed after the publication of these papers.
