弱ε-网的正分式交结果和变式
Positive-fraction intersection results and variations of weak epsilon-nets
摘要：
给定一个有限集$X$的点在$R^n$和家庭$F$的集合所产生的点对$X$，我们确定体积和结构条件的集合，使我们能够保证存在的正分数的子家庭$F'$的$F$的集合有非空的交集。这使我们能够证明这些家庭的弱ε网络的存在。我们还证明了凸集的弱ε-网的存在性的拓扑变化。
英文摘要：
Given a finite set $X$ of points in $R^n$ and a family $F$ of sets generated by the pairs of points of $X$, we determine volumetric and structural conditions for the sets that allow us to guarantee the existence of a positive-fraction subfamily $F'$ of $F$ for which the sets have non-empty intersection. This allows us to show the existence of weak epsilon-nets for these families. We also prove a topological variation of the existence of weak epsilon-nets for convex sets.
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。
