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November 16, 2003 POINTWISE CONVERGENCE ALONG CUBES FOR MEASURE
 

Summary: November 16, 2003
POINTWISE CONVERGENCE ALONG CUBES FOR MEASURE
PRESERVING SYSTEMS
BY I. ASSANI
Abstract. Let (X, B, ) be a probability measure space and T1, T2 , T3 three not neces-
sarily commuting measure preserving transformations on (X, B, ). We prove that for all
bounded functions f1, f2, f3 the averages
1
N2
N
n,m=1
f1(Tn
1 x)f2(Tm
2 x)f3(Tn+m
3 x)
converges a.e.. Generalizations to averages of 2k
- 1 functions are also given for not
necessarily commuting weakly mixing systems.
1. Introduction
In [A1] and [A2] we proved that if T is a measure preserving transformation on (X, B, )

  

Source: Assani, Idris - Department of Mathematics, University of North Carolina at Chapel Hill

 

Collections: Mathematics