I'm reading the article Sampling microfacet BRDF.
The GGX function is $D(h)$, the articles says the PDF respecting the spherical coordinates is $P_1(\theta)=D(h)Cos(\theta)Sin(\theta)$. But I think the PDF(in spherical coordinates) is $P_2(\theta)=D(h)Cos(\theta)$, where the term $Sin(\theta)$ is the Jacobian of integrator. Note that $\theta$ is the angle between normal vector and half vector.
Another intuitive feeling is that $P_1(0)=0$, $P_2(0)=D(h)$. I think $P_2$ seems more reasonable.
Is my understanding correct? Thanks.