Let Mn,m be the space of matrices of order n × m representing two-player zero-sum games in which Player I has n pure strategies and Player II has m pure strategies.

Prove that the function that associates with every matrix A = (a_ij ) ∈ M_n,m the value in mixed strategies of the game that it represents is continuous in (a_ij ).

Remark: The sequence of matrices (A^k)_k∈N in M_n,m, where to A = (a_ij ), if

a_ij = lim_k→∞ a^k_ij, ∀i,j.