Abstract:We study the pointwise asymptotic behaviour for the number of jumps of ergodic averages as the size of the oscillations decreases to zero. We find that under rather general conditions there exists a pointwise almost uniform asymptotics that relates the number and size of the jumps. The proof makes use of the upcrossing inequalities of Bishop.

Keywords:Cesaro averages. Upcrossing inequalities. Pointwise a.e. convergence. Asymptotics.