Structure in sets with logarithmic doubling
Abstract
Suppose that G is an abelian group, A is a finite subset of G with |A+A|< K|A| and eta in (0,1] is a parameter. Our main result is that there is a set L such that |A cap Span(L)| > K-Oeta(1)|A| and |L| = O(Keta log |A|). We include an application of this result to a generalisation of the Roth-Meshulam theorem due to Liu and Spencer.
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