You are currently browsing the tag archive for the ‘maximal inequality’ tag.

We continue our study of basic ergodic theorems, establishing the maximal and pointwise ergodic theorems of Birkhoff. Using these theorems, we can then give several equivalent notions of the fundamental concept of ergodicity, which (roughly speaking) plays the role in measure-preserving dynamics that minimality plays in topological dynamics. A general measure-preserving system is not necessarily ergodic, but we shall introduce the ergodic decomposition, which allows one to express any non-ergodic measure as an average of ergodic measures (generalising the decomposition of a permutation into disjoint cycles).

Read the rest of this entry »


RSS Google+ feed

  • An error has occurred; the feed is probably down. Try again later.

Get every new post delivered to your Inbox.

Join 3,314 other followers