In the present paper, a max-min theorem and a max theorem are proved on local convex topological linear spaces, as an ap摘要证明了局部凸线性拓扑空间上实值连续泛函的极大极小定理与极大定理，并由此证明了一类具有无限纯策略集的二人对策中最优混合策略的存在性。