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Random metric spaces and universality. (English. Russian original) Zbl 1065.60005

Russ. Math. Surv. 59, No. 2, 259-295 (2004); translation from Usp. Mat. Nauk 59, No. 2, 65-104 (2004).
The cone \(\mathcal R\) of distance matrices is defined as \[ \mathcal R :=\{(r_{ij})_{i,j=1}^\infty : r_{ii}=0,\;r_{ij}=r_{ji}\;,\; r_{ik}+r_{kj}\geq r_{ij}, \;i,j,k=1,2,\ldots\}. \] Each element in \(\mathcal R\) generates in a natural way a (semi)-distance on \(\mathbb N\). Certain Borel probability measures on \(\mathcal R\) are defined inductively by the so-called Markovian procedure. Properties of these measures are investigated and discussed.

MSC:

60B99 Probability theory on algebraic and topological structures
54E70 Probabilistic metric spaces
54E35 Metric spaces, metrizability
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