计盒维数积公式中的严格不等式
Strict inequality in the box-counting dimension product formulas
摘要：
已知笛卡儿积的上计盒维数满足不等式$\dim_{B}\left(F\times G\right)\leq \dim_{B}\left(F\right) + \dim_{B}\left(G\right)$，而下计盒维数满足不等式$\dim_{LB}\left(F\times G\right)\geq \dim_{LB}\left(F\right) + \dim_{LB}\left(G\right)$。我们构造Cantor类集合来证明这两个不等式都是严格的。
英文摘要：
It is known that the upper box-counting dimension of a Cartesian product satisfies the inequality $\dim_{B}\left(F\times G\right)\leq \dim_{B}\left(F\right) + \dim_{B}\left(G\right)$ whilst the lower box-counting dimension satisfies the inequality $\dim_{LB}\left(F\times G\right)\geq \dim_{LB}\left(F\right) + \dim_{LB}\left(G\right)$. We construct Cantor-like sets to demonstrate that both of these inequalities can be strict.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
