Ergodic Theorems for Nonconventional Arrays and an Extension of the Szemeredi Theorem

Yuri Kifer

The paper is primarily concerned with the asymptotic behavior as $N\to \infty$ of averages of nonconventional arrays having the form $N^{-1}\sum_{n=1}^N\prod_{j=1}^\ell T^{P_j(n,N)}…