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The Equivalence of Two Extremum Problems

Published online by Cambridge University Press:  20 November 2018

J. Kiefer  and
J. Wolfowitz
J. Kiefer
Affiliation:
Cornell University
J. Wolfowitz
Affiliation:
Cornell University
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 363 - 366
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Kiefer, J. and Wolfowitz, J., Optimum designs in regression problems, Ann. Math. Stat., 30 (1959).Google Scholar