Title: Universal characteristic factors and Furstenberg averages.

 Abstract: Averages of the form

  (1/N) sum_{n=1}^N f_1(T^nx)f_2(T^{2n}x)....f_k(T^{kn}x)

 were first introduced by Furstenberg in his ergodic theoretic proof of
 Szemeredi's theorem on arithmetic progressions.

 A factor of a measure preserving system is characteristic for an average
 if it "characterizes" the behavior of the average in the sense that the
 average can be calculated by projecting on that factor. We describe the
 universal characteristic factors of the above averages. Our construction
 is an alternative to the one given by Host & Kra.