DIMENSIONS OF THE POPCORN GRAPH

被引：2
|
作者：
Chen, Haipeng [1 ]
Fraser, Jonathan M. [2 ]
Yu, Han [3 ]
机构：
[1] Shenzhen Technol Univ, Coll Big Data & Internet, Shenzhen, Peoples R China
[2] Univ St Andrews, Math Inst, St Andrews, Scotland
[3] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge, England
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 11期
基金：
英国工程与自然科学研究理事会; 欧洲研究理事会;
关键词：
QUASI-ASSOUAD DIMENSION;
D O I：
10.1090/proc/15729
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The `popcorn function' is a well-known and important example in real analysis with many interesting features. We prove that the box dimension of the graph of the popcorn function is 4/3, as well as computing the Assouad dimension and Assouad spectrum. The main ingredients include Duffin-Schaeffer type estimates from Diophantine approximation and the Chung-Erdos inequality from probability theory.
引用
收藏
页码：4729 / 4742
页数：14
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