Abstract
Nonstandard methods are used to obtain results in combinatorial number theory. The main technique is to use the standard part map to translate density properties of subsets of ∗ N ^{\ast }\mathbb {N} into Lebesgue measure properties on [ 0 , 1 ] [0,1] . This allows us to obtain a simple condition on a standard sequence A A that guarantees the existence of intervals in arithmetic progression, all of which contain elements of A A with various uniform density conditions.
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