The Liouville map assigns to each point in the Teichm\"uller space a positive
Radon measure on the space of geodesics of the universal covering of the base
Riemann surface. This construction which was introduced by Bonahon is valid for
both finite and infinite Riemann surfaces. Bonahon and S\"ozen proved that the
Liouville map is differentiable for closed Riemann surfaces and the second
author extended this result to all other Riemann surfaces. Otal proved that the
Liouville map is real analytic using an idea from the geometric analysis. The
purpose of this note is to give another proof of Otal's result using a complex
analysis approach.Comment: 15 pages, Lemma 6 adde