The primary aim of this work is to introduce a new class of functions called µ-(ω, c)-pseudo almost periodic functions. Using the measure theory, we generalize in a natural way some recent works and study some properties of those µ-(ω, c)-pseudo almost periodic functions including two new composition results which play a crucial role for the existence of some µ-(ω, c)-pseudo almost periodic solutions of certain semilinear differential equations and partial differential equations. We also investigate the existence and uniqueness of the µ-(ω, c)pseudo almost periodic solutions for some models of Lasota-Wazewska equation with measure (ω, c)-pseudo almost periodic coefficient and mixed delays.