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, Annali di Matematica pura ed applicata, (IV) CLXV (1993) 133-158].