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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.