# Monthly Archives: July 2011

## Szemerèdi Regularity Lemma

Welcome to the first in our series about Great Lemmas of Mathematics. We’ll start with one of the greats from combinatorics, perhaps the most useful tool in combinatorics and graph theory: the Szemerèdi Regularity Lemma (SRL). This was first proved … Continue reading

## Rudin’s inequality

After that whirlwind tour through Khintchine’s inequality, let’s take a look at the less well-known Rudin’s inequality. This says (at least in one form) that, given a finite abelian group and a function if the support of the Fourier transform … Continue reading

## Khintchine’s inequality

It was recently suggested to me that the proof of Khintchine’s inequality is one which I should think about deeply, and I would especially like to explore the relationship between Khintchine’s and Rudin’s inequality. This will be the first of … Continue reading

## What does additive structure mean?

Suppose we have a finite subset of an abelian group, and I told you it was additively structured. There are lots of different things this vague term could mean: The set is not much bigger than . There are lots … Continue reading