Monthly Archives: May 2012

Covering the natural numbers with generalized arithmetic progressions

In this short post I will present some curious facts I came across recently. Given a real number construct the set , where, as usual, denotes the floor function. Note that if is an integer, then is an (infinite) arithmetic … Continue reading

Posted in Combinatorics | Tagged | 2 Comments

Koopman-von Neumann Decomposition

In my previous post I presented an ergodic theoretical proof of Roth’s Theorem, assuming the Koopman-von Neumann Decomposition (and some other minor facts). In this post I present a proof of this Decomposition and moreover prove that the compact vectors … Continue reading

Posted in Ergodic Theory | Tagged , , , | 4 Comments