Radon-Nikodym derivative ($d\nu /d\mu$)

When $\nu \ll \mu$, the Radon-Nikodym derivative is the almost-everywhere unique measurable function satisfying $\nu (A)={\int }_A(d\nu /d\mu )d\mu$.

For an absolutely continuous change of probability measure, restricting its Radon-Nikodym derivative to the current sigma-algebra gives this nonnegative uniformly integrable martingale. If $Z_T>0$ almost surely, the measures are equivalent on ${\mathcal{F}}_T$. This finite-horizon equivalence need not imply equivalence on a larger sigma-algebra.