Theorems in measure theory

Vitali convergence theorem

In real analysis and measure theory, the Vitali convergence theorem, named after the Italian mathematician Giuseppe Vitali, is a generalization of the better-known dominated convergence theorem of Henri Lebesgue. It is a characterization of the convergence in Lp in terms of convergence in measure and a condition related to uniform integrability. (Wikipedia).

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Related pages

Uniform integrability | Real analysis | Measure space | Lp space | Dominated convergence theorem | Henri Lebesgue | Giuseppe Vitali