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.