Note sur la continuit\'e de la projection dans les facteurs de Host-Kra

Abstract

B. Host and B. Kra (2005) have introduced the characteristic factors for studying cubic ergodic averages. These factors allow one to resolve, in particular, multiple recurrence problems introduced by H. Furstenberg (1977). We show here that the continuity of the projection of the system in its characteristic factors characterises cubic averages.