An $L^1$ counting problem in ergodic theory

Idris Assani, Zoltan Buczolich, Daniel Mauldin

We solve the following counting problem for measure preserving transformations. For $f\in L_{+}^1(\mu )$, is it true that $\ds \sup_n\frac{\bN_n(f)(x)}{n} <\infty,$ where $$\ds\bN_n(f)(…