No abstract

UDC 517.9 Our aim is to present the concept of double-measure ergodic and double-measure pseudo almost periodic functions  in Stepanov's sense.  In addition, we present numerous interesting results, such as the composition theorems and completeness properties for these two  spaces of the considered functions.  We also establish the  existence and  uniqueness for the  double-measure pseudo almost periodic mild solutions  in Stepanov's sense for some evolution equations.