Mixture-space theorem

In microeconomic theory and decision theory, the Mixture-space theorem is a utility-representation theorem for preferences defined over general mixture spaces.

The theorem generalizes the von Neumann–Morgenstern utility theorem and the usual utility-representation theorem for consumer preferences over ${\displaystyle \mathbb {R} ^{n}}$. It was first proven by Israel Nathan Herstein and John Milnor in 1953, together with the introduction of the definition of a mixture space.