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DISTANCE GEOMETRY IN QUASIHYPERMETRIC SPACES. I
2009
Bulletin of the Australian Mathematical Society
Let (X, d) be a compact metric space and let M(X ) denote the space of all finite signed Borel measures on X . Define I : M(X ) → R by and set M(X ) = sup I (µ), where µ ranges over the collection of signed measures in M(X ) of total mass 1. The metric space (X, d) is quasihypermetric if for all n ∈ N, all α 1 , . . . , α n ∈ R satisfying n i=1 α i = 0 and all x 1 , . . . , x n ∈ X , the inequality n i, j=1 α i α j d(x i , x j ) ≤ 0 holds. Without the quasihypermetric property M(X ) is
doi:10.1017/s0004972708000932
fatcat:ncyso4dmwrfzblyboj5apu3tvm