On the norm convergence of non-conventional ergodic averages
On the norm convergence of non-conventional ergodic averages
Abstract We offer a proof of the following non-conventional ergodic theorem: If T i :ℤ r ↷( X ,Σ, μ ) for i =1,2,…, d are commuting probability-preserving ℤ r -actions, ( I N ) N ≥1 is a Følner sequence of subsets of ℤ r , ( a N …