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Abstract
In real Euclidean n Rn where r denotes the distance of a given point in Rn to the origin 0, it is well known that if the law of gravitational attration is proportional to 4n-1, then the attraction due to a uniform spherical shell with centre 0 is the same as the attraction due to the mass of the shell concentrated at 0. In this paper, it is shown that if this mean value property holds for all such spheres, then the law of force is given by for some constants A and B. Furthermore, in certain cases, by use of the theory of mean periodic functions, it is shown that this law of force holds when this mean value property holds for just two spheres.