Definition (Differential divergence)

This is identical to divergence, where for RVs $X$ and $Y$ with pdfs $f_{X}, f_{Y}$, with supports $S_{X}\subset S_{Y}\subset \mathbb{R}$. Then the divergence between $X$ and $Y$ is $$\begin{align*} D(X\|Y):&=E_{f_{X}}\left[\log_{2}\frac{f_{X}(X)}{f_{Y}(Y)}\right]\\\\ &=\int_{S_{X}}f_{X}(t)\log_{2}\frac{f_{X}(t)}{f_{Y}(t)}dt \end{align*}$$ Multivariate version: $$D(X^{n}\|Y^{n}):=\int_{S_{X^{n}}}f_{X^{n}}(t_{1},\cdots,t_{n})\log_{2}\frac{f_{X^{n}}(t_{1},\cdots,t_{n})}{f_{Y^{n}}(t_{1},\cdots,t_{n})}dt_{1}\cdots dt_{n}$$