AI 中文总结
该研究证明可能无限的3-图族的均匀Turán密度集合Π₃,∞包含终端区间[1−δ,1]，进而得出其具有正勒贝格测度和豪斯多夫维数1的结论。
AI 中文摘要
我们证明，可能无限的3-图族的均匀Turán密度集合Π₃,∞包含一个终端区间：存在δ>0，使得[1−δ,1]⊆Π₃,∞。因此，Π₃,∞具有正的勒贝格测度和豪斯多夫维数1。
英文摘要
We prove that the set $Π_{\therefore,\infty}$ of uniform Turán densities of possibly infinite families of $3$-graphs contains a terminal interval: there exists $δ>0$ such that $[1-δ,1]\subseteqΠ_{\therefore,\infty}$. Consequently, $Π_{\therefore,\infty}$ has positive Lebesgue measure and Hausdorff dimension $1$.
Comments19pp, comments are welcome
