Let IR n be Euclidean n-space with generic element x = (x 1 . . . . , x.) and let C(]R") be the space of continuous complex-valued functions f : IR ~ ~ r under the topology of uniform convergence on compact subsets of IR ~. A function f in C(IR ~) is said to be mean periodic if the span of the ordinary translates of f is not dense in C(IR"). There is an extensive literature on the subject of mean periodic functions. Clearly, there is a corresponding notion of "mean automorphic" functions associated with each semigroup of mappings of IR ~ into IRL Let H be the group of homeomorphisms qJ that map IR n onto ]R" in the following special way: