Monthly Archives: February 2013

Jin’s Theorem

— 1. Introduction — The Poincaré recurrence theorem (or, more accurately, its proof) implies that, given a set with positive upper Banach density, i.e. then there exists some such that . In fact one gets that the set of those … Continue reading

Posted in Combinatorics, Ergodic Theory, Ramsey Theory | Tagged , , , , , , | 2 Comments

Weak Mixing

— 1. Introduction — When studying measure preserving systems (defined below) there are many important classes that are worth studying separately. One way to distinguish between different classes is the level of “mixing” or “randomness” of the system. In this … Continue reading

Posted in Analysis, Ergodic Theory | Tagged , , , , | 2 Comments