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