Sets with Prescribed Arithmetic Densities
نویسندگان
چکیده
Using concepts of generalized asymptotic and logarithmic densities based on weighted arithmetic means over an arithmetical semigroup G we prove that under some additional technical assumptions on the weighted counting function of its elements, a subset of G exists with all four generalized densities (upper and lower asymptotic and logarithmic) prescribed subject to the natural condition 0 ≤ d(A) ≤ `(A) ≤ `(A) ≤ d(A) ≤ 1. Communicated by Ladislav Mǐśık
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تاریخ انتشار 2008