Dubins–Spanier theorems

The Dubins–Spanier theorems are several theorems in the theory of fair cake-cutting. They were published by Lester Dubins and Edwin Spanier in 1961. Although the original motivation for these theorems is fair division, they are in fact general theorems in measure theory.

There is a set ${\displaystyle U}$, and a set ${\displaystyle \mathbb {U} }$ which is a sigma-algebra of subsets of ${\displaystyle U}$.

There are ${\displaystyle n}$ partners. Every partner ${\displaystyle i}$ has a personal value measure ${\displaystyle V_{i}:\mathbb {U} \to \mathbb {R} }$. This function determines how much each subset of ${\displaystyle U}$ is worth to that partner.

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