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Cake-cutting is a playful name for the fair division of a heterogeneous,divisible good among agents, a well-studied problem at the intersection ofmathematics, economics, and artificial intelligence. The cake-cuttingliterature is rich and edifying. However, different model assumptions are madein its many papers, in particular regarding the set of allowed pieces of cakethat are to be distributed among the agents and regarding the agents' valuationfunctions by which they measure these pieces. We survey the commonly useddefinitions in the cake-cutting literature, highlight their strengths andweaknesses, and make some recommendations on what definitions could be mostreasonably used when looking through the lens of measure theory.

Cutting a Cake Is Not Always a 'Piece of Cake': A Closer Look at the Foundations of Cake-Cutting Through the Lens of Measure Theory