What is meant by finite action signal In section 1.3 from Signals, Systems and Inference, Alan V. Oppenheim, George C. Verghese. Finite-action signals, which are also called absolutely summable signals, are defined by the condition
\begin{equation}
 \int_{-\infty}^{\infty}|x(t)|dt&lt;\infty
\end{equation}
whereas for discrete time signal, its as
\begin{equation}
 \sum_{k = -\infty}^{\infty}|x[k]|&lt;\infty
\end{equation}
The integration and sum on the left are called the action of the signal. Therefore also known as finite-action signals.
So I would like to know what does finite action signal means? Or is there intuitive explanation about it.
It's something like "finite energy signals"

$$ \int_{-\infty}^{\infty}|x(t)|^2 dt&lt;\infty $$

$$ \sum_{n=-\infty}^{\infty}|x[n]|^2 &lt;\infty $$

except that the "finiteness" is a tougher constraint with

$$ \int_{-\infty}^{\infty}|x(t)| dt&lt;\infty $$

$$ \sum_{n=-\infty}^{\infty}|x[n]| &lt;\infty $$

for example, the signal

$$ x(t) = \frac{1}{\sqrt{1+t^2}} $$

is finite energy, but is not finite action.