280 
(67) 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
o, 
E> 
here 
EL ow 
T,)E, 
(T, — 
ts 
xpd 
then 
= 
58) 
Je 
| (æ,) dt > — 
> (T, TT 
T,) 02%, 
=) 
Proof: We define 
pr) = 7 = - measure of } {| T, <t<T, and a; <x 
Then p(o)=o0, p(co)=1, and, from (67) and x,>o , 
0 oo 2E oo 
69) E> TT | = NE dote) = [x dpa) “fe dp. (x) > 
r, 1 0 2 
> 0 + 2% (1 — p(2£)) 
Likewise, from the nonincreasing property of (x), 
(70) 
a a ( ) 2 
ax x) du(x + (æ) du. x 
| “ 2k oO 
x T J o( 2) . 2, 
Since, from (69), (28)= — , (70) implies (68). 
"41 Koopmans - pag. 56