Abstract
member of the family of straight lines A1x1 + A2x2 + A3 = 0. More generally, a hyperplane in n-dimensional space is usually necessary for n+ 1 variables. By permitting more complicated instruments it may be possible to reduce the number of dimensions in which the instrument operates. The theorem to be given does precisely this by selecting the instrument from a certain family of hypersurfaces. DEFINITION. If f is a function of n variables sl, * * *, Sn and can be expressed by an n by n determinant (V,j) where Vij is a function of si only, then f will be called a nomogramic disjunctive function, or simply an N-function. DEFINITION. Let R' be a function of the single variable si for k=1, * , m and for i1, = *, n. Let gj be a function of m variables ul, * * *, urn for j= 1, * * *, n. We shall say that the triple (m, Rt, gj) belongs to f if f is an N-function with 1
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