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This theorem is useless unless equation (27) can be established, and, if one wishes to prove this by imitating the procedure used for Theorem 4, then the following features have to be verified, subject to assumptions. It is possible to arrange the ordering { ym} in such a manner that for a sequence of integers Tn --we have 1 Tn M{f(P)} = lim -T fE(ymp) (28) n--co Tn n=l uniformly for P in U0. Also, the union of sets Tn E um m=0 constitutes a piece of space whose actual boundary consists of several sufficiently smooth surfaces whose two-dimensional induced surface area is o(Tn) as n -a 0.Remark 4: Finally, we note that, with the aid of the mean (27), we may even obtain the statement on emptiness itself without requiring almost-periodicity at all. Assume that for a certain mean (28) we may go over from equation (25) to equation (26); that relation (22) holds; and that we have not only equation (27) but also M7{fu0 *At dv} = -My {Ifuo giJ ij dv} in analogy to equation (14); then -IR > 0 implies that V4 is empty.1 Theories relativistes de la gravitation et de l'4lectromagndtisme (Paris: Masson & Cie, 1955).