Abstract A natural method how to measure sets of natural numbers is the asymptotic density which is a special case of weighted densities. These densities are based on the Riesz summation method. A completely different approach is the Abel summation method. This leads to the concept of the Abel density. In this paper we prove estimates of the values of the lower and upper Abel densities, depending on values of the lower and upper asymptotic densities.

中文翻译：

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关于渐近密度和阿贝尔密度的关系

摘要 度量自然数集的一种自然方法是渐近密度，它是加权密度的一个特例。这些密度基于 Riesz 求和方法。一种完全不同的方法是 Abel 求和法。这引出了阿贝尔密度的概念。在本文中，我们根据下渐近密度和上渐近密度的值证明了下阿贝尔密度和上阿贝尔密度的估计值。