Probability Theory and Related Fields

, Volume 114, Issue 3, pp 401–417

A generalized strong law of large numbers

  • Ana Colubi
  • Miguel López-Díiaz
  • J. Santos Domíinguez-Menchero
  • M. Angeles Gil

DOI: 10.1007/s004400050229

Cite this article as:
Colubi, A., López-Díiaz, M., Domíinguez-Menchero, J. et al. Probab Theory Relat Fields (1999) 114: 401. doi:10.1007/s004400050229

Abstract.

Strong laws of large numbers have been stated in the literature for measurable functions taking on values on different spaces. In this paper, a strong law of large numbers which generalizes some previous ones (like those for real-valued random variables and compact random sets) is established. This law is an example of a strong law of large numbers for Borel measurable nonseparably valued elements of a metric space.

Mathematics Subject Classification (1991): Primary 60F15; Secondary 03B52, 60D05 

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Ana Colubi
    • 1
  • Miguel López-Díiaz
    • 1
  • J. Santos Domíinguez-Menchero
    • 1
  • M. Angeles Gil
    • 1
  1. 1.Departamento de Estadística, I.O. y D.M., Universidad de Oviedo, C/Calvo Sotelo, s/n, E-33007 Oviedo, Spain. e-mail: jsdm@pinon.ccu.uniovi.esES