Totally probabilistic $L^p$ 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 $L^p$ 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.


Volume 4, Issue 2 - Serial Number 2
October 2013
Pages 78-88
  • Receive Date: 05 June 2013
  • Revise Date: 01 September 2013
  • Accept Date: 08 September 2013