[Authors]
 A. M. Vershik

[Title]
 Universality and randomness for the graphs and metric spaces

[AMS Subj-class]
 54E35 Metric spaces, metrizability
 05C50 Graphs and matrices
 60D05 Geometric probability, stochastic geometry, random sets

[Abstract]
 We consider the universal graph (R. Rado) and universal metric
 space (P. Urysohn) from new point of view and then define
 the corresponding random objects. For the graphs, an old theorem
 by Erdos-Renji claimed that with probabilty one this graph is universal.
 We generalize this theorem and extend it to the case of  metric spaces.

[Comments]
 LaTeX, English, 19 pp.

[Contact e-mail]
 vershik@pdmi.ras.ru