A 𝐷_{𝐸}[0,1] representation of random upper semicontinuous functions

Colubi, Ana; Domínguez-Menchero, J.; López-Díaz, Miguel; Ralescu, Dan

doi:10.1090/S0002-9939-02-06429-8

A $D_E[0,1]$ representation of random upper semicontinuous functions
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by Ana Colubi, J. S. Domínguez-Menchero, Miguel López-Díaz and Dan Ralescu

Proc. Amer. Math. Soc. 130 (2002), 3237-3242

DOI: https://doi.org/10.1090/S0002-9939-02-06429-8

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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