Let {S1, S2,..., Sn} be a collection of nonempty (possibly non convex) subsets of an m-dimensional linear space, and let

Then
1.

2.

where

3.

with bij ‰¥ 0 and bij > 0 for at most m + n components.
5. Define

Then i = conv Si and

Show that all but at most i actually belong to Si.

, 1, ei E ei