SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIOUE ETC. 
28; 
Proof of (K). We again distinguish the three cases with 
regard to the asymptotic range of z,, used in the proof of (B). 
Case (1), £<&. In this case Proposition (K) is equivalent 
to Lemma 2. 
Case (2), {=8=ty#2. For definiteness assume Ç<2 and 
let 2-¢=3e. Since now lim z,=G we can choose T such that 
ta 
(71) 
10r 
A 
and at the same time large enough for there to exist an attain- 
able path (x}, 2;) on [o, T] such that z°=zr+e. For {=T we 
choose (x3, 2) according to 
(72) 
x, + g(27) —2(z) for all t=T 
Then, (x},2}) is attainable throughout, and from (42), (71), 
for t=T, 
(73) x" - 
- g(a 
ow LV ay a \~, 
Ho 1878) * € 
Hence for 
(74) «Was (=, 
p- 
WU...) 
-U VUE) 
rd 8 
i (arty 
(Xr — 
£1 
u(y) dt 
On the other hand, by (36), (40 a), (71), 
[4] Koopmans - pag. ,