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