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.

翻译：蛋糕切割是对异质可分割物品在智能体间进行公平分配的戏称，这是数学、经济学与人工智能交叉领域中的经典研究问题。相关文献丰富且具有启发性，但诸多论文采用了不同的模型假设，尤其体现在可供分配给智能体的蛋糕片集合设定，以及智能体用于衡量这些蛋糕片的估值函数方面。本文梳理了蛋糕切割文献中常用的定义，阐明其优势与不足，并从测度论视角提出若干关于定义最合理使用的建议。