A Quantitative Ergodic Theory Proof of Szemerédi's Theorem
A Quantitative Ergodic Theory Proof of Szemerédi's Theorem
A famous theorem of Szemerédi asserts that given any density $0 < \delta \leq 1$ and any integer $k \geq 3$, any set of integers with density $\delta$ will contain infinitely many proper arithmetic progressions of length $k$. For general $k$ there are essentially four known proofs of this fact; …