The aim of this work is to present new concept of Stepanov-Like -Cn-pseudo almost periodic of class r using the measure theory. We use the (μ, ν)-ergodic functions to define the spaces of (μ, ν) Stepanov-Like-Cn-pseudo almost periodic functions of class r. We present many interesting results on those spaces like completeness and composition theorems and we study the existence and the uniqueness of the (μ, ν) Stepanov-Like-Cn pseudo almost periodic solutions of class r for of the evolution equation. We provide an example to illustrate ours results.

Measure theory, (μ, ν)-pseudo almost periodic function, partial functional differential equations.