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Inverse problem for upper asymptotic density |
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| Authors: | Renling Jin |
| Affiliation: | Department of Mathematics, College of Charleston, Charleston, South Carolina 29424 |
| Abstract: | For a set  of natural numbers, the structural properties are described when the upper asymptotic density of  achieves the infimum of the upper asymptotic densities of all sets of the form  , where the upper asymptotic density of  is greater than or equal to the upper asymptotic density of  . As a corollary, we prove that if the upper asymptotic density of  is less than  and the upper asymptotic density of  achieves the infimum, then the lower asymptotic density of  must be  . |
| Keywords: | Upper asymptotic density inverse problem nonstandard analysis |
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