论文标题
在$ C_0 $ - 等效性和系列排列
On the $c_0$-equivalence and permutations of series
论文作者
论文摘要
假设一个收敛的实数系列$ \ sum \ limits_ {n = 1}^\ infty a_n $具有存在一个集合$ a \ subseteq \ n $的属性，以使得$ \ sum \ sum \ sum \ limits_ {n \ in a} a_n $ in} a_n $有条件地转化。 We prove that for a given arbitrary sequence $(b_n)$ of real numbers there exists a permutation $σ\colon \N \to \N$ such that $σ(n) = n$ for every $n \notin A$ and $(b_n)$ is $c_0$-equivalent to a subsequence of the sequence of partial sums of the series $ \ sum \ limits_ {n = 1}^\ infty a_ {σ（n）} $。 此外，我们讨论了我们的主要结果与经典的Riemann系列定理之间的联系。
Assume that a convergent series of real numbers $\sum\limits_{n=1}^\infty a_n$ has the property that there exists a set $A\subseteq \N$ such that the series $\sum\limits_{n \in A} a_n$ is conditionally convergent. We prove that for a given arbitrary sequence $(b_n)$ of real numbers there exists a permutation $σ\colon \N \to \N$ such that $σ(n) = n$ for every $n \notin A$ and $(b_n)$ is $c_0$-equivalent to a subsequence of the sequence of partial sums of the series $\sum\limits_{n=1}^\infty a_{σ(n)}$. Moreover, we discuss a connection between our main result with the classical Riemann series theorem.
