In this paper we derive some results concerning the relation between ordinary pointwise convergence, convergence in the sense of Schwartz distributions (weak convergence), and norm convergence of ...

We prove pointwise convergence, as N → ∞, for the multiple ergodic averages $(1/\mathrm{N})\sum _{\mathrm{n}=1}^{\mathrm{N}}\mathrm{f}\left({\mathrm{T}}^{\mathrm ...