Another Proof of a Freĭman-type Theorem
نویسنده
چکیده
We provide a new proof of a Frĕıman-type theorem. Specifically, suppose that G is a locally compact abelian group with a Haar measure μG. The δ-ball Bδ of a translation invariant metric is called d-dimensional if μG(B2δ′ ) 6 2 dμG(Bδ′ ) for all δ ′ ∈ (0, δ]. We show that if A is a compact neighborhood with μG(nA) 6 n μG(A) for all n > d log d, then A is contained in a O(d log d)-dimensional ball, B, of some translation invariant metric and μG(B) 6 exp(O(d log d))μG(A).
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