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The Equivalence of Two Extremum Problems

  • J. Kiefer (a1) and J. Wolfowitz (a1)
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Let f1 , …, fk be linearly independent real functions on a space X, such that the range R of (f1, …, fk) is a compact set in k dimensional Euclidean space. (This will happen, for example, if the fi are continuous and X is a compact topological space.) Let S be any Borel field of subsets of X which includes X and all sets which consist of a finite number of points, and let C = {ε} be any class of probability measures on S which includes all probability measures with finite support (that is, which assign probability one to a set consisting of a finite number of points), and which are such that

is defined. In all that follows we consider only probability measures ε which are in C.

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References
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1. Kiefer, J. and Wolfowitz, J., Optimum designs in regression problems, Ann. Math. Stat., 30 (1959).
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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