A basic measure of the combinatorial complexity of a convexity space is its Radon number. In this paper we answer a question of Kalai, by showing a fractional Helly theorem for convexity spaces with bounded Radon number. As a consequence we also get a weak ε-net theorem for convexity spaces with bounded Radon number. This answers a question of Bukh and extends a recent result of Moran and Yehudayoff.

中文翻译：

---

数和分数阶Helly定理

凸空间的组合复杂度的基本度量是其Radon数。在本文中，我们通过显示有界Radon数的凸空间的分数阶Helly定理，回答了Kalai的问题。结果，对于有界Radon数的凸空间，我们也得到了一个弱ε- net定理。这回答了Bukh的问题，并扩展了Moran和Yehudayoff的最新结果。