PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
73) 
T4 T+ 
tai dt = ER 23 <(T*—1)2 
provided T* - T=1 and §=%+2¢. It follows from (75) and 
Assumption (e) that x7 and «(x*) when substituted for x, and 
p(x) in Lemma 4 satisfy the premises of that lemma on the 
interval [T, T*]. Hence, from (74), (68), 
I A 
Ws (~0) 2, n-u(22 + 4e) - (T* — T) eoT 
from which (K) follows directly. The proof for $< ¢ is similar. 
Case (3), &={=2. For any e>o, subject still to later 
choice, there now exists an integer T such that 
76) 
5 
e<z2,<g2+e¢ for t=T 
It will be useful to write tWrs(- 0) as the difference of 
two integrals 
- 
4 y; 
r* T* 
Ways (-0) = | eo ur) =) dt — fee ut) =) dt = 
; ; 
= Uns (—7) — i. § J (—0) 
Taking first the second term we have, from (43 a) with x; = À. 
(36) and (38 a). 
"47 Koopmans - pag. 58