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.