论文标题
尾巴概率和发散系列
Tail Probability and Divergent Series
论文作者
论文摘要
从主要的理论考虑来看，我们表明，对于每个非负，有限和$ l^{1} $在给定有限的度量空间上起作用，存在一些非平凡的真实数字顺序，以至于从真实的序言和任何有分歧的一系列no的序言中获得的序列汇总而不是积极的一系列范围，而不是像积极的一系列的范围，那样的范围和诸如“范围”集成了一个范围的概述。在不平等方面，这些含义增加了有关数学期望的附加信息以及带正面，消失的求和的发散序列的行为，并从广义上建立了概率理论与数字理论之间的一些新的，出乎意料的联系。
From mostly a measure-theoretic consideration, we show that for every nonnegative, finite, and $L^{1}$ function on a given finite measure space there is some nontrivial sequence of real numbers such that the series, obtained from summing over the term-by-term products of the reals and the summands of any divergent series with positive, vanishing summands such as the harmonic series, is convergent and no greater than the integral of the function. In terms of inequalities, the implications add additional information on mathematical expectation and the behavior of divergent series with positive, vanishing summands, and establish in a broad sense some new, unexpected connections between probability theory and, for instance, number theory.
