论文标题
中央康托尔设置为cantorval的差异的条件
Conditions for the difference set of a central Cantor set to be a Cantorval
论文作者
论文摘要
令$ c（λ）\ subset \ lbrack 0,1] $表示由序列$λ= \ left生成的中央cantor集（λ_{n} \ right）\ in \ left（0，\ frac {1} {1} {1} {2} {2} {2} {2} {2} {2} {2} {2} \ right）通过已知的三分法，$ c（λ）$的差异集$ c（λ）-c（λ）$是三个可能的集合之一：封闭间隔的有限结合，cantor套件和一个cantorval。我们的主要结果描述了$（λ_{n}）$的有效条件，这些条件保证了$ c（λ）-c（λ）$是cantorval。我们表明这些条件可以以几种等效形式表示。在其他假设下，建立了Cantorval $ C（λ）-c（λ）$的度量。我们为一些快速收敛系列的成就集提供了证明定理的应用。
Let $C(λ)\subset \lbrack 0,1]$ denote the central Cantor set generated by a sequence $ λ= \left( λ_{n} \right) \in \left( 0,\frac{1}{2} \right) ^{\mathbb{N}}$. By the known trichotomy, the difference set $ C(λ)-C(λ)$ of $C(λ)$ is one of three possible sets: a finite union of closed intervals, a Cantor set, and a Cantorval. Our main result describes effective conditions for $(λ_{n})$ which guarantee that $C(λ)-C(λ)$ is a Cantorval. We show that these conditions can be expressed in several equivalent forms. Under additional assumptions, the measure of the Cantorval $C(λ)-C(λ)$ is established. We give an application of the proved theorems for the achievement sets of some fast convergent series.
