= Meridional velocity isotropy of a two-integral distribution
{title2=$\langle v_R^2\rangle=\langle v_z^2\rangle$}
At fixed position a <two-integral distribution> depends on $v_R,v_z$ only through $v_R^2+v_z^2$. Swapping these integration variables makes their second moments equal. Their odd moments and mixed second moments vanish by reflection symmetry. For an even function of $L_z$ the azimuthal <velocity> is also centered, so all mixed entries of the <velocity ellipsoid> vanish.
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