g(x) = \min_{y\in B}f(x,y)
h(y) = \max_{x\in A}f(x,y)
\forall x,y \in A,B \space \space g(x) \le f(x,y), \space h(y) \ge f(x,y)
\therefore g(x) \le f(x,y) \le h(y)
And,
\max_{x\in A} \min_{y\in B} f(x,y) \le \min_{y\in B} \max_{x \in A} f(x,y)
Is this correct?