 
Summary: Pointwise characteristic factors for the
multiterm return times theorem
Idris Assani, Kimberly Presser
Department of Mathematics, UNC Chapel Hill, NC 27599,
(email: assani@math.unc.edu)
Department of Mathematics, Shippensburg University, PA 27517
(email: kjpres@ship.edu)
(Received December 30, 2010)
Abstract. This paper is an update and extension of a result the authors first proved
in 2003. The goal of this paper is to study factors which are known to be L2

characteristic for certain nonconventional averages and prove that these factors are
pointwise characteristic for the multiterm return times averages.
In memory of Dan Rudolph.
Pointwise Characteristic Factors 1
1. Introduction
A major result in ergodic theory in the late 1980's was the proof of the return
times theorem by J. Bourgain [8] (which was later simplified by J. Bourgain,
H. Furstenberg, Y. Katznelson, D. Ornstein in [9]). This theorem created a key
strengthening of the Birkhoff's Pointwise Ergodic Theorem [7].
