MEAN (µ, ν)-PSEUDO ALMOST PERIODIC SOLUTIONS OF CLASS r UNDER THE ANGLE OF MEASURE THEORY TO SOME STOCHASTIC EVOLUTION EQUATIONS

MEAN (µ, ν)-PSEUDO ALMOST PERIODIC SOLUTIONS OF CLASS r UNDER THE ANGLE OF MEASURE THEORY TO SOME STOCHASTIC EVOLUTION EQUATIONS

The paper introduces and studies the concept of mean (µ, ν)-pseudo almost periodic solution of class r for stochastic processes using the measure theory. We use (µ, ν)-ergodic process to define the spaces of (µ, ν)-pseudo almost periodic processes of class r in the mean sense. We also present many interesting results on this spaces, such as completeness and composition theorems. Our abstract results are subsequently applied to investigate the existence and uniqueness of mean almost pseudo periodic solutions for the stochastic evolution equation.