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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A $D_E[0,1]$ representation of random upper semicontinuous functions


Authors: Ana Colubi, J. S. Domínguez-Menchero, Miguel López-Díaz and Dan Ralescu
Journal: Proc. Amer. Math. Soc. 130 (2002), 3237-3242
MSC (1991): Primary 49J45, 60B99, 28A20, 54C35
Published electronically: March 25, 2002
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Abstract: In this paper a representation of random upper semicontinuous functions in terms of $D_E[0,1]$-valued random elements is stated. This fact allows us to consider for the first time a complete and separable metric, the Skorohod one, on a wide class of upper semicontinuous functions. Finally, different relevant concepts of measurability for random upper semicontinuous functions are studied and the relationships between them are analyzed.


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Additional Information

Ana Colubi
Affiliation: Departamento de Estadstica e IO, Universidad de Oviedo, 33071, Oviedo, Spain
Email: colubi@pinon.ccu.uniovi.es

J. S. Domínguez-Menchero
Affiliation: Departamento de Estadstica e IO, Universidad de Oviedo, 33071, Oviedo, Spain
Email: jsdm@pinon.ccu.uniovi.es

Miguel López-Díaz
Affiliation: Departamento de Estadstica e IO, Universidad de Oviedo, 33071, Oviedo, Spain
Email: mld@pinon.ccu.uniovi.es

Dan Ralescu
Affiliation: Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221
Email: Dan.Ralescu@math.uc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06429-8
PII: S 0002-9939(02)06429-8
Keywords: Cadlag function, measurability, Random upper semicontinuous function, Skorohod metric, uniform metric
Received by editor(s): March 2, 2000
Received by editor(s) in revised form: June 1, 2001
Published electronically: March 25, 2002
Additional Notes: The work of the first, second and third authors was partially supported by the Spanish DGESYC (MEC) Grants No. PB95-1049, No. PB97-1282 and PB98-1534.
The work of the fourth author was partially supported by the NSF Grant MRI 9871345 and by the STA Fellowship 398049.
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2002 American Mathematical Society