Total Energy:
$ E_{\infty} = \int^{\infty}_{-\infty} |x(t)|^2 dt = \lim_{T\to\infty} \int^T_{-T} |x(t)|^2 dt $
Average Power:
$ P_{\infty} = \lim_{T\to\infty} \frac{1}{2T} \int^T_{-T} |x(t)|^2 dt $
Therefore if
$ E_{\infty} < \infty $,
$ P_{\infty} = \lim_{T\to\infty} \frac{E_{\infty}}{2T} = 0 $
-Bill Snow
