In the recent papers  and , we introduced some new techniques for constructing an extension of a probability-preserving system T: ℤd ↷ (X, µ) that enjoys certain desirable properties in connexion with the asymptotic behaviour of some related nonconventional ergodic averages.
The present paper is the first of two that explore various refinements and extensions of these ideas. This first part is dedicated to some much more general machinery for the construction of extensions that can be used to recover the results of [1, 2]. It also contains two relatively simple new applications of this machinery to the study of certain families of nonconventional averages, one in discrete and one in continuous time (convergence being a new result for the latter).
ASJC Scopus subject areas