  In this note, we derive a Mellin space version of the Lorentzian inversion
formula for CFTs by explicitly integrating over the cross-ratios in $d=2$ and
$d=4$ spacetime dimensions. We use the simplicity of the Mellin representation
of Witten diagrams and the double discontinuity to find the OPE coefficients
and anomalous dimensions of double-trace primaries in large $N$ CFTs to order
$\frac{1}{N^4}$. We find that our results match analytically at order
$\frac{1}{N^2}$, and numerically at order $\frac{1}{N^4}$ with existing
literature.
