Monthly Archives: April 2012

Proof of Roth’s Theorem using Ergodic Theory

In 1975 Szemerédi proved what is now known as Szemerédi’s theorem on arithmetic progressions, answering an old question by Erdös and Turán. Twenty years earlier Roth had proved the (much simpler) case of arithmetic progressions of length 3. Theorem 1 … Continue reading

Posted in Ergodic Theory, Ramsey Theory | 12 Comments

Recurrence theorems

Let be a probability space and let be a (measurable) map such that for any (measurable) set we have , where as usual . Such is called a measure preserving transformation. In this setting, all sets in the pre-orbit of … Continue reading

Posted in Ergodic Theory | 6 Comments