where ® is defined by 
SP (t,t) = £ (te) O(e, 1) (1.19) 
Now consider the difference in the values of the cost function; by 
GE) 
(E 
il D@s, > W)) = BW], 45 W) do + C(xns T) - C(Za> 2) = © 
0 
Hence, from the assumptions on F and G, 
TE 
{ [P_ OS se EG) = B@)]) cde + E_Ox(t) > © 
J oo ry re a 
By (1.18), 
T 
iD 
{ ERA) i OG, CS) Gao) > £@©) pido Cae) riGiGe)) ieee 
0 0 
aE 
+6 { 0(T, o) (E(u(o)) - £(v(c))) do > 0 (1.20) 
0 
If the order of integration in the double integral is changed, 
it T 
{ Ba Gp) i OG nO) LEG @) eet Gio) adodyn 
Oi 0 
T T 
= i i F(t) O(t, OC) di Guo) eae Gn) sido Glo ZL) 
0 o 
The vector function p. is defined by 
a 
pute) & = | a) OG, =) tr = CG) O@, &) G22) 
t= 
Recall that one of the properties of ® was (1.15) 
oe (t, t) = - O(n, t) £ (ct) 
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