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  "body": "\n## Statement\n\nThe Ruzsa covering lemma states the following:\n\nLet $A$ and $S$ be finite subsets of an [[abelian group|071DDFVG4J]] with $S$ nonempty, and let $K$ be a positive real number. Then if $|A+S| \\le K|S|$, there is a subset $T$ of $A$ with at most $K$ elements such that $A \\subseteq T+S-S$.\n\nThis lemma provides a bound on how many copies of $S-S$ one needs to cover $A$, hence the name. The proof is essentially a greedy algorithm:\n",
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