On dominated convergence

Dominated Convergence for Fuzzy Random Variables

dominated convergence for fuzzy random variables

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A metastable dominated convergence theorem

The dominated convergence theorem implies that if (fn) is a sequence of functions on a probability space taking values in the interval [0, 1], and (fn) converges pointwise a.e., then ( ∫ fn) converges to the integral of the pointwise limit. Tao [26] has proved a quantitative version of this theorem: given a uniform bound on the rates of metastable convergence in the hypothesis, there is a bound...

dominated convergence for fuzzy random variables

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 ...