Before revision:  That is , there is a set of m k-flats, such that any convex body in [0,1]^d of volume larger than \eps is stabbed by one of these k-flats.
After revision:  That is , there is a set of k-flats, such that any convex body in [0,1]^d of volume larger than \eps is stabbed by one of these k-flats.