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