On completeness of the space of weighted pseudo almost automorphic functions

In this paper, we prove that for every ρ∈U∞ρ∈U∞, the space of weighted pseudo almost automorphic functions is complete under the supremum norm. This gives an affirmative answer to a key and fundamental problem for weighted pseudo almost automorphic functions, and fills a gap in the proof of Liu and Song (2010) [9].