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The Density of the Set of Sums

Imre Z. Ruzsa

出版	DIMACS, Center for Discrete Mathematics and Theoretical Computer Science, 1989
URL	http://books.google.com.hk/books?id=Vh3gHwAACAAJ&hl=&source=gbs_api

註釋

Abstract: "Let 1 [less than or equal to] a1 [less than or equal to] a2 [less than or equal to] ... be a sequence of integers, and let S be the set of all sums of the form [sum of]e[subscript i]a[subscript i] where e1 = 0 or 1. Affirming a conjecture of P. Erdʺos, we prove that if a[subscript n+1] [less than or equal to] 2a[subscript n] for all but a finite number of the subscripts n, then S has a (positive) asymptotic density."