M. Núñez y J.
Rojo

*Situaciones y métricas
aleatorias*

pp. 775-778 in

*IX Jornadas Matemáticas Hispano-Lusas, Salamanca, 1982*

Abstract:

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