Lorentzian Curve: Is It Normalized?

[Sirben4]

Is a lorentzian curve by definition normalized? As far as I can tell it is such that ∫L(x) = 1.

 

[Mandelbroth]

Is a lorentzian curve by definition normalized? As far as I can tell it is such that ∫L(x) = 1.

If we define it as $L(x) = \frac{1}{\pi} \frac{\frac{1}{2} \Gamma}{(x-x_0)^2 + (\frac{1}{2} \Gamma)^2}$, then $\displaystyle \int_{-\infty}^{\infty} L(x) \ dx = 1$.