Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4662373 | Annals of Pure and Applied Logic | 2012 | 11 Pages |
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].
► We present a proof of Lebesgue’s dominated convergence theorem. ► The proof is presented in the abstract setting of ordered uniform spaces. ► The proof is done constructively in intuitionistic logic and in Bishop’s style. ► We do not employ any axiom of choice or impredicative construction. ► The proof generalises and makes constructive Weber’s proof for uniform lattices.