Dellwo David R
3912 Lienz Lane, College Station, TX 77845, USA.
Heliyon. 2023 Apr 1;9(5):e14862. doi: 10.1016/j.heliyon.2023.e14862. eCollection 2023 May.
The terms fat and skinny in the title are vernacular references to Cantor sets of positive and zero measure respectively. The paper demonstrates that a fat Cantor subset of , , possesses a skinny companion that forms a Cantor subset of where is the total length of all the gaps associated with the ternary construction of the fat Cantor set. Moreover, elements of the fat Cantor set can be decomposed and expressed as the sum of two components. One of the components is an element of . The other component is an element of the skinny companion contained in .
标题中的“胖”和“瘦”分别是对正测度和零测度康托集的通俗说法。本文证明，[具体空间]中的一个胖康托子集拥有一个瘦伴随集，该瘦伴随集构成[另一具体空间]的一个康托子集，其中[具体变量]是与胖康托集的三进制构造相关的所有间隙的总长度。此外，胖康托集的元素可以分解并表示为两个分量的和。其中一个分量是[某空间]的一个元素。另一个分量是包含在[另一空间]中的瘦伴随集的一个元素。
