Probabilistic Normed Spaces (PN spaces) have recently been redefined by Alsina, Schweizer and Sklar. We begin the study of these spaces by giving several examples; in particular we (a) present a detailed study of $\alpha$-simple spaces, (b) construct a PN space on the vector space of (equivalence classes) of random variable and (c) show that its probabilistic norm alone generates the the norms of all $L^p$- and Orlicz spaces.
Some Classes of Probabilistic Normed Spaces
SEMPI, Carlo
1997-01-01
Abstract
Probabilistic Normed Spaces (PN spaces) have recently been redefined by Alsina, Schweizer and Sklar. We begin the study of these spaces by giving several examples; in particular we (a) present a detailed study of $\alpha$-simple spaces, (b) construct a PN space on the vector space of (equivalence classes) of random variable and (c) show that its probabilistic norm alone generates the the norms of all $L^p$- and Orlicz spaces.File in questo prodotto:
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