Page:Elementary Principles in Statistical Mechanics (1902).djvu/162

or

$\int \ldots \int (\Delta \eta e^{\Delta \eta }-e^{\Delta \eta }+1)\,dp_{1}\ldots dq_{n}>0.$

(454)

Since the parenthesis in this expression represents a positive value, except when it vanishes for $\Delta \eta =0$, the integral will be positive unless $\Delta \eta$ vanishes everywhere within the limits, which would make the difference of the two distributions vanish. The theorem is therefore proved.