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We first give a solution to a key problem concerning the completeness of the space of weighted pseudo almost-periodic functions and then establish a new composition theorem with respect to these functions. Some important remarks with concrete examples are also presented. Moreover, we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation: x′(t)=Ax(t)+f(t,x(t)), t∈ℝ, where A is the infinitesimal generator of an exponentially stable C0-semigroup. An application is also given to illustrate the abstract existence theorem.