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A \(D_E[0,1]\) representation of random upper semicontinuous functions. (English) Zbl 1005.28003

Summary: 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.

MSC:

28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
54E50 Complete metric spaces
49J45 Methods involving semicontinuity and convergence; relaxation
60B99 Probability theory on algebraic and topological structures
60F05 Central limit and other weak theorems
54C35 Function spaces in general topology
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