
Recent Posts
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
Koopmanvon Neumann Decomposition
In my previous post I presented an ergodic theoretical proof of Roth’s Theorem, assuming the Koopmanvon 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