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P. EVANS and F. J. GOULD [1], H. J. GREENBERG and W. P. PIERSKALLA [2], R. R. MEYER [1], W. W. ROGAN [3], and others. r r, 36 3. 1. c. 1. °. Proof. °. c. on X X {A O}. d. 2. c. functions on X X {A O}. ° and the set FAo is compact and non empty. Proof. 3. °. ° with (M n F) At \ Q =1= () Vt. Let xt be, for all t, elements of the above difference set. ° there exist yt E FAo with d(xt, yt) -+ 0, t -+ 00. Furthermore, there exists in the compact set FAo an accumulation point XO of all yt which at the same time must be an accumulation point of the sequence {xt}.

3 be weakened as follows: For eachi = 1, ... , s there exists a finite number of convex weakly analytic functions hki : fEn ~ IR , ki ,pi, = 1, ... and gi is given by gi(X) = max {hk;(x) I ki = 1, ... 3 then remains valid. Proof. M(A) may be written as M(A) = {x j = I hkj(x) E fEn 8 ~ Ai, i + 1, ... ,m} . = 1, ... The corollary then follows from the theorem. ,8, k, = 1, ... 3, and that the hypotheses of the theorem do not imply that M is upper semicontinuous (H). Consider the following function g(xv x 2 ) = IX21 {0 e-(x,lIx,1) ~f Xl ~ 0, If Xl ~ 0 , if Xl:::;; 0 .

X/} n X' . 17) > > < > > » Hence NJ,x'(f(x' = {x E X' If(x)

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