Minimax Theorems and Their Proofs

We suppose that X and Y are nonempty sets and f: X x Y →IR A minimax theorem is a theorem which asserts that, under certain conditions, $$\mathop{{\min }}\limits_{Y} \mathop{{\max }}\limits_{X} f = \mathop{{\max }}\limits_{X} \mathop{{\min }}\limits_{Y} f.$$

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