TY - JOUR
T1 - Pleasant extensions retaining algebraic structure, I
AU - Austin, Tim
N1 - Publisher Copyright:
© 2015, Hebrew University Magnes Press.
PY - 2015/1
Y1 - 2015/1
N2 - In the recent papers [1] and [2], 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).
AB - In the recent papers [1] and [2], 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).
UR - http://www.scopus.com/inward/record.url?scp=84922495921&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84922495921&partnerID=8YFLogxK
U2 - 10.1007/s11854-015-0001-9
DO - 10.1007/s11854-015-0001-9
M3 - Article
AN - SCOPUS:84922495921
SN - 0021-7670
VL - 125
SP - 1
EP - 36
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
IS - 1
ER -