论文标题
关于总和的密度，ii
On the density of sumsets, II
论文作者
论文摘要
算术准依赖性是在$ \ mathbb {n} $的功率集中部分定义的一个真实值集的大型家族，包括渐近密度，Banach密度，分析密度等。 令$ b \ subseteq \ mathbb {n} $为非空套，覆盖$ O（n！）$残留类modulo $ n！$ as $ n \ to \ to \ infty $（例如，Primes或Perfect Powers）。我们表明，对于[0,1] $中的每一个$α\，都有一个$ a \ subseteq \ mathbb {n} $，这样，对于每个算术quasi-dementy $μ$，$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a + b $均在$ $ $ $ $中，此外，以及，$μ（$ $ $ $（A + b）= a $ b）= c。证明依赖于1946年首先考虑的鲜为人知的密度的性质。
Arithmetic quasi-densities are a large family of real-valued set functions partially defined on the power set of $\mathbb{N}$, including the asymptotic density, the Banach density, the analytic density, etc. Let $B \subseteq \mathbb{N}$ be a non-empty set covering $o(n!)$ residue classes modulo $n!$ as $n\to \infty$ (e.g., the primes or the perfect powers). We show that, for each $α\in [0,1]$, there is a set $A\subseteq \mathbb{N}$ such that, for every arithmetic quasi-density $μ$, both $A$ and the sumset $A+B$ are in the domain of $μ$ and, in addition, $μ(A + B) = α$. The proof relies on the properties of a little known density first considered by Buck in 1946.
