Fr x c r TO

= - I 1 — exp—J J (1 — e-Xu) v (u,s) duds)) —

Derivatives with respect to A of the functions Lo(A,x) and Lc(A,x) are continuous in A and decrease. It follows L'c(A,x) — L'o(A,x). Actually,

1 (Lc(A, x) — Lc(A — h,x)) > L'c(A, x) > 1 (Lc(A + h,x) — Lc(A, x)), h h

1 (Lo(A, x) — Lo(A — h, x)) > L'o(A, x) > 1 (Lo(A + h,x) — Lo(A, x)). h h

Hence

L'c(A,x) — Lo(A, x) < 1 (Lc(A,x) — Lc(A — h,x)) — 1 (Lo(A + h,x) — Lo(A,x)), hh

Lo(A, x) — L'c(A,x) < 1 (Lo(A,x) — Lo(A — h,x)) — 1 (Lc(A + h,x) — Lc(A,x)) h h and consequently,

IL'c(A,x) — Lo(A,x)l < 1 (Lo(A,x) — Lo(A — h,x)) —1 (Lo(A+h,x) — Lo(A,x))+ hh

+ 1 ILcXA,x) — Lo (A, x)l + 1 ILc(A — h,x) — Lo(A — h,x)l + hh

+1 ILdA + h,x) — Lo(A + h,x)l = eh + £c(h), h wher eh — 0 as h — 0 and for any h > 0 ec(h) — 0 as c — 0. Consequently, uniformly in A < Ao r u e-Xu du - r u e-Xu v(u,x)

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