Totally probabilistic L^p spaces

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_۰. It is also shown that if the distribution p satisfies p > \varepsilon_۱ then, as in the classical case, these spaces are complete probabilistic normed spaces.

Keywords:

probabilistic normed space , probabilistic valued measure , probabilistic L^p spaces