SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 275
where #(z) denotes the inverse of z, on [o, T], and x(2)=x,,.
The unknown function is now x(z), defined, like #(z), on the
interval 2,<z<{2, or on 2<z=z, as the case may be. The
advantage from the change of variables lies in the fact that
only x(z) itself, and no derivative thereof, occur in the inte-
grand in (60). Hence (60) is maximized on the set of superior
paths if and only if x(z) is given a value £*(2) such that the
integrand is maximized for almost every value of z in its do-
main. This requires £*(z) for almost every z to equal the solu-
tion x =x(z) of
‘61,
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21H
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Koopmans - pag. 49