The paper by Kiefer and Wolfowitz establishes the equivalence of two extremum problems in the context of probability measures on a space X. The first problem is to choose a probability measure ξ that maximizes the determinant of the matrix M(ξ), which is formed by the integrals of products of functions f_i(x) with respect to ξ. The second problem is to choose a probability measure ξ that minimizes the maximum value of a quadratic form d(x; ξ) over x. The paper also shows that a sufficient condition for the second problem is that the maximum value of d(x; ξ) equals k. The main result is that these three conditions are equivalent. This result strengthens and extends previous work on optimal design of regression experiments. The proof involves showing that the set of all ξ satisfying these conditions is linear and that the matrix M(ξ) is the same for all such ξ. A corollary is that there exists a probability measure ξ and a linear transformation g_i such that the functions g_1, ..., g_k are orthonormal with respect to ξ and the maximum of the sum of squares of g_i(x) over x is equal to k. The paper also discusses extensions and applications, including statistical applications in regression experiments where the goal is to choose an optimal design. The equivalence of two optimality criteria is shown, and it is noted that the results have practical importance in the design of experiments. The paper concludes with a brief description of the statistical applications and the importance of the equivalence of the two criteria in obtaining optimal solutions.The paper by Kiefer and Wolfowitz establishes the equivalence of two extremum problems in the context of probability measures on a space X. The first problem is to choose a probability measure ξ that maximizes the determinant of the matrix M(ξ), which is formed by the integrals of products of functions f_i(x) with respect to ξ. The second problem is to choose a probability measure ξ that minimizes the maximum value of a quadratic form d(x; ξ) over x. The paper also shows that a sufficient condition for the second problem is that the maximum value of d(x; ξ) equals k. The main result is that these three conditions are equivalent. This result strengthens and extends previous work on optimal design of regression experiments. The proof involves showing that the set of all ξ satisfying these conditions is linear and that the matrix M(ξ) is the same for all such ξ. A corollary is that there exists a probability measure ξ and a linear transformation g_i such that the functions g_1, ..., g_k are orthonormal with respect to ξ and the maximum of the sum of squares of g_i(x) over x is equal to k. The paper also discusses extensions and applications, including statistical applications in regression experiments where the goal is to choose an optimal design. The equivalence of two optimality criteria is shown, and it is noted that the results have practical importance in the design of experiments. The paper concludes with a brief description of the statistical applications and the importance of the equivalence of the two criteria in obtaining optimal solutions.