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Tag Archives: factor
Szemerédi’s Theorem Part II – Overview of the proof
This is the second in a series of posts about Szemerédi’s theorem. In the first post I presented the first step in the proof of Szemerédi’ theorem, namely applying the correspondence principle of Furstenberg to transform the problem into one … Continue reading
Posted in Combinatorics, Ergodic Theory
Tagged almost periodic, cesaro limit, Extension, factor, Furstenberg, Syndetic sets, Szemerédi, Szemeredi's theorem, weak mixing
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Sated extensions
I recently learned of a promising technique in ergodic Ramsey theory that is useful to establish multiple recurrence and convergence of nonconventional ergodic averages. The trick is to reduce the general statement to certain systems, called sated systems. A common … 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