Let be the semi-direct product of and , and let us consider the product group , . For a large class of probability measures on , one proves that there exists such that the sequence of finite measures
converges weakly to a nondegenerate measure.
Cite this article
Emile Le Page, Marc Peigné, Local limit theorems on some non unimodular groups. Rev. Mat. Iberoam. 15 (1999), no. 1, pp. 117–141