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§ 1. Lecture Notes aim to report new developments -quickly, informally, and at a high level. The texts should be reasonably self-contained and rounded off. Thus they may, and often will, present not only results of the author but also related work by other people. Furthermore, the manuscripts should provide sufficient motivation, examples and applications. This clearly distinguishes Lecture Notes manuscripts from journal articles which normally are very concise. Articles intended for ajournal but too long to be accepted by most journals, usually do not have this "lecture notes" character. For similar reasons it is unusual for Ph. D. theses to be accepted for the Lecture Notes series.

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This paper is concerned with pseudo almost automorphic functions, which are more general and complicated than pseudo almost periodic functions and asymptotically almost automorphic functions. New results, concerning the composition of pseudo almost automorphic functions, are established.