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- W3100802950 abstract "We provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if $Asubseteq mathbb{N}$ has positive Banach logarithmic density, then $A$ contains an approximate geometric progression of any length. We also prove that if $A,Bsubseteq mathbb{N}$ have positive Banach logarithmic density, then there are arbitrarily long intervals whose gaps on $Acdot B$ are multiplicatively bounded, a multiplicative version Jin's sumset theorem. The main technical tool is the use of a quotient of a Loeb measure space with respect to a multiplicative cut." @default.
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- W3100802950 date "2016-09-14" @default.
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- W3100802950 title "A monad measure space for logarithmic density" @default.
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- W3100802950 doi "https://doi.org/10.1007/s00605-016-0966-1" @default.
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