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By W. W. Sawyer

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Ii) Let V = U { U~~. s;; r: U~~. }. 14) suppTs;; v-. iii) lfy E suppTwe shall assume that cp(y) '# 0 and obtain a contradiction. There is an open relatively compact neighborhood W of y such that cp is not 0 on W and so, as above, T = 0 on W. 14). d. 9 Radon measures are synthesizable. The following is a standard measure-theoretic fact [Bourbaki, 1, pp. 68-71]. 2. a) Given T E D0 (r) and assume cp E Cc(r) vanishes on suppT. Then (T, cp) =0. l~~. l,. = .. Proof. We shall prove a). i) Set K = supp cp and E = supp T.

D. 5 Standard characterizations of S-sets. Define MiE) = {JL E M(E):cardsupp JL <

2, so that I(M) s k(E) from a). 9, M = M(I(M)) 2 M(k(E)) = A;(E). d. 5 Standard characterizations of S-sets. Define MiE) = {JL E M(E):cardsupp JL <

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