### Totally probabilistic $L^p$ spaces

Document Type : Research Paper

Authors

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

Abstract

In this paper, we introduce the notion of probabilistic valued measures as a generalization of non-negative measures and construct the corresponding $L^p$ spaces, for distributions $p > \varepsilon_0$. It is also shown that if the distribution $p$ satisfies $p > \varepsilon_1$ then, as in the classical case, these spaces are complete probabilistic normed spaces.

Keywords