= Flux-limited galaxy selection
{title2=$V_{\max}\propto L^{3/2}$}
For a nearby Euclidean survey with limiting <flux> $f_{\min}$, a <galaxy> of <luminosity> $L$ is detectable out to $d_{\max}=\sqrt{L/(4\pi f_{\min})}$. Its accessible volume is therefore proportional to $L^{3/2}$. With a <Schechter function> $\phi(L)\propto L^\alpha e^{-L/L_*}$, counts per logarithmic interval are proportional to $L^{\alpha+5/2}e^{-L/L_*}$ and peak at $(\alpha+5/2)L_*$ when $\alpha>-5/2$. This selection suppresses faint objects relative to a volume-limited census; finite survey boundaries and cosmological evolution modify the simple law.
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