6 D . J . NEWMA N
(L23) g(x)ax + b\ogx.
Since a is clearly positiv e w e may se t x = I/a i n (1.23) and thereb y obtai n 1 + b
log(lAz). Henc e g(x) ax + log(l/z) - 1, by (1.23), and w e get
re~^x)dxa
r
el-axdx
= ae-- = e,
Jo Jo a
which i s (1.22). Q.E.D.
A pleasant joke, thi s last one ; the us e of th e principl e o f th e separatin g hyperplane t o
derive a concrete inequality .
La commedia et finita
Notes on Lectur e I
For informatio n o n th e appropriate limi t theorem s of probability theor y one may con-
sult e.g .
W. Feller, An introduction to probability theory and its applications. Vol. 1, Wiley,
New York, 1957, p. 139.
D. J. Newma n an d T. J. Rivlin , Approximation of monomials by lower degree poly-
nomials, Aequationes Math . 14 (1976), 451-455.
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