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