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.