Sion's minimax theorem

In mathematics, and in particular game theory, Sion's minimax theorem is a generalization of John von Neumann's minimax theorem, named after Maurice Sion.

It states:

Let ${\displaystyle X}$ be a compact convex subset of a linear topological space and ${\displaystyle Y}$ a convex subset of a linear topological space. If ${\displaystyle f}$ is a real-valued function on ${\displaystyle X\times Y}$ with

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