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