Totally probabilistic Lp spaces

Document Type : Research Paper


Department of Mathematical Sciences, Isfahan university of Technology, Isfahan 84156 83111, Iran.


In this paper, we introduce the notion of probabilistic valued measures as a generalization of non-
negative measures and construct the corresponding Lp spaces, for distributions p > "0. It is also
shown that if the distribution p satis es p  "1 then, as in the classical case, these spaces are complete
probabilistic normed spaces.