Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665486 | Advances in Mathematics | 2015 | 33 Pages |
Abstract
Renling Jin proved that if A and B are two subsets of the natural numbers with positive Banach density, then A+BA+B is piecewise syndetic. In this paper, we prove that, under various assumptions on positive lower or upper densities of A and B , there is a high density set of witnesses to the piecewise syndeticity of A+BA+B. Most of the results are shown to hold more generally for subsets of ZdZd. The key technical tool is a Lebesgue density theorem for measure spaces induced by cuts in the nonstandard integers.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Mauro Di Nasso, Isaac Goldbring, Renling Jin, Steven Leth, Martino Lupini, Karl Mahlburg,