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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
T*-1 
(81) LUss_,(~0) = est (g(2+n) —g9(2))dt >— u,y n° 57* (es(T*-D_ goT) = 
— 94! 2 ——4 96T* 
> u yn Ge 
For T* - 1=<¢<T*, x varies and must be boxed in. 
0 ee, OCNÉN,, We have from (70 b), (38), 
If 
x*=min {g(t -¢), g3+n)-e x, <t+e +n = a 
where €, 7, are chosen small enough to make #*>0. Then, 
because # (x) decreases with x, 
“=max uw @*), uo J=u' (x) > #(@*)=u">0 for T* - 1=<¢t<T. 
We therefore have from (79 b), (80), 
352) 
+ Us (—5) = fe u (x?) (g(et) — 9) — 2#) dt > 
T+_1 
> —U' y n° e0T* Lu” - (a —3) eo TT 
Pulling together these inequalities we have, for any T**=T* 
from (79 c), (77), (78), (81), (82), since w'=u’ >i, 
Wop (<6) > |—u' (yn? (1 +671) + 2:) +u'(n—e) e-s|eo1* = A esT* , say. 
[4] Koopmans - pag. 60