A DE[0,1] Representation of Random Upper Semicontinuous Functions

In this paper a representation of random upper semicontinuous functions in terms of DE[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 re...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2002-11, Vol.130 (11), p.3237-3242
Main Authors: Colubi, Ana, Domínguez-Menchero, J. S., López-Díaz, Miguel, Ralescu, Dan
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Exact sciences and technology
General topology
Mathematical analysis
Mathematical functions
Mathematical theorems
Mathematics
Measurability
Measure and integration
Probabilities
Probability and statistics
Probability theory and stochastic processes
Probability theory on algebraic and topological structures
Random variables
Sciences and techniques of general use
Separable spaces
Topological spaces
Topological theorems
Topology
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In this paper a representation of random upper semicontinuous functions in terms of DE[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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-02-06429-8