Lebesgue's dominated convergence theorem in Bishop's style

We present a constructive proof in Bishop’s style of Lebesgue’s dominated convergence theorem in the abstract setting of ordered uniform spaces. The proof generalises to this setting a classical proof in the framework of uniform lattices presented by Hans Weber in “Uniform Lattices II: Order Continuity and Exhaustivity”, in Annali di Matematica Pura ed Applicata (IV), Vol. CLXV (1993). 1. Both authors have been partially supported by DAMA (Dimostrazione Assistita per la Matematica e l’Apprendimento), a strategic project of the University of Bologna. 2. Department of Computer Science, University of Bologna, Mura A. Zamboni 7, 40127 Bologna, Italy.