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EnglishWe provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if A⊆ N has positive Banach logarithmic density, then A contains an approximate geometric progression of any length. We also prove that if A, B⊆ N have positive Banach logarithmic density, then there are arbitrarily long intervals whose gaps on A· 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.
A monad measure space for logarithmic density / Di Nasso, Mauro; Goldbring, Isaac; Jin, Renling; Leth, Steven; Lupini, Martino; Mahlburg, Karl. - In: MONATSHEFTE FÜR MATHEMATIK. - ISSN 0026-9255. - STAMPA. - 181:3(2016), pp. 577-599.
| Autori interni: | |
| Autori: | Di Nasso, Mauro; Goldbring, Isaac; Jin, Renling; Leth, Steven; Lupini, Martino; Mahlburg, Karl |
| Titolo: | A monad measure space for logarithmic density |
| Anno del prodotto: | 2016 |
| Abstract: | We provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if A⊆ N has positive Banach logarithmic density, then A contains an approximate geometric progression of any length. We also prove that if A, B⊆ N have positive Banach logarithmic density, then there are arbitrarily long intervals whose gaps on A· 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. |
| Digital Object Identifier (DOI): | 10.1007/s00605-016-0966-1 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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