We prove variations of Carath\'eodory's, Helly's and Tverberg's theorems
where the sets involved are measured according to continuous functions such as
the volume or diameter. Among our results, we present continuous quantitative
versions of Lov\'asz's colorful Helly theorem, B\'ar\'any's colorful
Carath\'eodory's theorem, and the colorful Tverberg theorem.Comment: 22 pages. arXiv admin note: substantial text overlap with
arXiv:1503.0611
