Relative entropy bound for the unnormalized Hellinger distance
= Relative entropy bound for the unnormalized Hellinger distance
{title2=$H^2(P,Q)\leq K(P,Q)$}
The scalar inequality $-\log u\geq1-u$, applied to $u=\sqrt{q/p}$ and integrated against $P$, gives $K(P,Q)\geq2-2\int\sqrt{pq}\,d\mu$. The right side is the unnormalized squared <Hellinger distance>. Infinite divergence and zero density regions are handled by the usual extended-integral conventions.