integrable function is almost everywhere equal to the limit of its average over balls. The proof uses weak-type estimates and maximal functions to control the almost everywhere convergence.

Ergodic theory

Harmonic analysis is used in classical results of ergodic theory. The maximal ergodic theorem is analogous to the Hardy-Littlewood maximal theorem: it bounds the measure of the set on which a supremum of ergodic averages is large. Such

1.Previous
3.Next