The notion of (k,m)-agreeable society was introduced by Deborah Berg et al.:a family of convex subsets of R is called (k,m)-agreeable if any subfamily of size m contains at least one non-empty k-fold intersection. In that paper, the (k,m)-agreeability of a convex family was shown to imply the existence of a subfamily of size βn with non-empty intersection, where n is the size of the original fa...
