  In this paper, we prove some finiteness results about split Kac-Moody groups
over local non-archimedean fields. Our results generalize those of "An affine
Gindikin-Karpelevich formula" by Alexander Braverman, Howard Garland, David
Kazhdan and Manish Patnaik. We do not require our groups to be affine. We use
the hovel I associated to this situation, which is the analogue of the
Bruhat-Tits building for a reductive group.
