WEIGHTS FOR THE ERGODIC MAXIMAL OPERATOR AND AE CONVERGENCE OF THE ERGODIC AVERAGES FOR FUNCTIONS IN LORENTZ SPACES

In this paper, we deal with an invertible null-preserving transformation into itself of a finite measure space. We prove that the uniform boundedness of the ergodic averages in a reflexive Lorentz space implies a.e. convergence. In order to do this, we study the ''good weights'' for the maximal operator associated to an invertible measure preserving transformation.