Fair Division without Additivity

for all disjoint pieces A, B, and C. Finally, strong continuity says that the cake can be crumbled into "arbitrarily small" pieces. The problem is to divide the cake so that everybody is satisfied with the share she receives. We mention the classical works of Steinhaus [8] and Dubins and Spanier [3] dealing with this problem, and point readers to Brams and Taylor [2] and Robertson and Webb [6] for complete references.