The objective in this work is to present a new concept of p-th mean pseudo almost automorphic by use of the measure theory. We use the ( µ,ν)-ergodic process to define the spaces of ( µ,ν)-pseudo almost automorphic process of class r in the p-th sense. To do this, firstly we show some interesting results regarding the completeness and composition theorems. Secondly we study the existence, uniqueness of the p-th mean ( µ,ν)-pseudo almost automorphic solution of class r for the stochastic evolution equation. AMS Subject Classification : 60H15 ; 60G20 ; 34K30 ; 34K50 ; 43A60.

The aim of this work is to present new approach to study weighted pseudo almost periodic functions with infinite delay using the measure theory. We study the existence and uniqueness of (μ,ν)-pseudo almost periodic solutions of infinite class for some neutral partial functional differential equations in a Banach space when the delay is distributed on ]-∞,0].