Almost everywhere convergence and recurrence along subsequences in ergodic theory

Let A be a set of natural numbers. For x ;Recently the circle method has found applications in ergodic theory. Let T be a measure preserving transformation of the probability space (;The question of almost everywhere convergence of the averages M;While Bourgain examined the a.e convergence of K;We also show that the ergodic averages along the prime numbers converge a.e. for any f ;In the second part of this dissertation we examine sets of recurrence. A set R of integers is called a set of recurrence if for any measure preserving transformation T of the probability space (...