## A quantitative improvement for Roth's theorem on arithmetic progressions

- Thomas F. Bloom
- J. London Math. Society
- 2016

@article{Lee2017CoveringTL, title={Covering the Large Spectrum and Generalized Riesz Products}, author={James R. Lee}, journal={SIAM J. Discrete Math.}, year={2017}, volume={31}, pages={562-572} }

- Published 2017 in SIAM J. Discrete Math.
DOI:10.1137/15M1048604

Chang’s Lemma is a widely employed result in additive combinatorics. It gives optimal bounds on the dimension of the large spectrum of probability distributions on nite abelian groups. In this note, we show how Chang’s Lemma and a powerful variant due to Bloom both follow easily from an approximation theorem for probability measures in terms of generalized Riesz products. The latter result involves no algebraic structure. The proofs are correspondingly elementary.