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 ...

Pointwise Convergence: A mode of convergence in function spaces where convergence is determined by the behaviour of functions at each individual point.

N. Frantzikinakis, E. Lesigne, M. Wierdl, Random Sequences and Pointwise Convergence of Multiple Ergodic Averages, Indiana University Mathematics Journal, Vol. 61, No ...

Modern pointwise ergodic theory developed largely out of the work of Bourgain in the late 80s and early 90s, but recent efforts over the past 10 years have seen the field develop in new directions, as ...