  We generalize a theorem of Tate and show that the second cohomology of the
Weil group of a global or local field with coefficients in $\C^*$ (or more
generally, with coefficients in the complex points of a tori over $\C$) vanish,
where the cohomology groups are defined using measurable cochains in the sense
of Moore. We recover a theorem of Labesse proving that admissible homomorphisms
of a Weil group to the Langlands dual of a reductive group can be lifted to an
extension of the Langlands dual group by a tori.
