M. Núñez y J. Rojo
Situaciones y métricas aleatorias
pp. 775-778 in
IX Jornadas Matemáticas Hispano-Lusas, Salamanca, 1982

We assign to every point of a set X a Radon measure s_x on R^n, considering that it describes in a diffuse way the location of x. We define a random metric F on X, which is shown to verify the next theorem: let (x_n) be a nonconstant sequence converging with e-level of security to x. Then there exists z in R^n such that s_x({z})>=1-e. Moreover, if e<1/2, z is unique, and for every r>0, lim_inf s_x_n(B(z,r))>=1-e. Hence, if that is true for every e, s_x must be a Dirac measure.
AMS(MOS) subject classification: 54J05

Preprint file as PDF situac.pdf