752 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
From (110-10), (122-1) and (123-5) we have 
© Li'l 
(123-8) | £ = T (0) db = y. [Fer (ng) df 
0 Jo 
Thus developing (123-8) as a Taylor series 
ow [ 2 3 - i , 
(123-9) / | Or due [poas=1. / | Ly 
“0 2! 3! o L 21 
bz 8 
2 
+. [a(@y dé 
Thus from (112-1) 
(123-10) 
‘oo ge 2 8 
sou t fPTa8 84 Jos 
Ce vA 2 31! 
and finally 
(123-11) 
Yeo 0 - [7 
T—7 — + =; vo 4 
74, #1 (e** — T — 7’6)p(6)d6 
Thus necessarily 
(123-12) 0 s— To _ 
L— (1-Pp) Ye 
for 1-o0>o0 
Whatever the function ¢(8) this inequality is very important 
for empirical analysis. 
11] Allais - pag. 56