Generalized random fields and Lévy's continuity Theorem on the space of tempered distributions
Résumé
In this note, we recall main properties of generalized random fields and present a proof of the continuity theorem of Paul Lévy for generalized random fields in the space of tempered distributions. This theorem was first proved by Fernique in a more general setting. The aim of this note is to provide a self-contained proof that in particular avoids the abstract theory of nuclear spaces.
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