  We show quantitative versions of classic results in discrete geometry, where
the size of a convex set is determined by some non-negative function. We give
versions of this kind for the selection theorem of B\'ar\'any, the existence of
weak epsilon-nets for convex sets and the $(p,q)$ theorem of Alon and Kleitman.
These methods can be applied to functions such as the volume, surface area or
number of points of a discrete set. We also give general quantitative versions
of the colorful Helly theorem for continuous functions.
