= Euclidean accessible-volume luminosity weighting
{c}
{title2=$V_{\max}\propto L^{3/2}$}
For a <flux> threshold $f_{\min}$ and isotropic point-source <luminosity> $L$, the detection radius is $r_{\max}=\sqrt{L/(4\pi f_{\min})}$. In a homogeneous Euclidean population the accessible volume is proportional to $L^{3/2}$, so the selected <luminosity> distribution is proportional to $\varphi(L)L^{3/2}$. This assumes <flux> selection and inverse-square propagation, not an arbitrary surface-brightness-selected diffuse field.
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