  The Brownian loop measure is a conformally invariant measure on loops in the
plane that arises when studying the Schramm-Loewner evolution (SLE). When an
SLE curve in a domain evolves from an interior point, it is natural to consider
the loops that hit the curve and leave the domain, but their measure is
infinite. We show that there is a related normalized quantity that is finite
and invariant under M\"obius transformations of the plane. We estimate this
quantity when the curve is small and the domain simply connected. We then use
this estimate to prove a formula for the Radon-Nikodym derivative of reversed
radial SLE with respect to whole-plane SLE.
