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The first proof of this theorem was given by Camille Jordan in his lectures on real analysis, and was published in his book Cours d'analyse de l'École Polytechnique.
In his academic work, Lorch focused on several subfields of classical analysis such as summability theory, Fourier analysis, ordinary differential equations and real analysis.
Professor David W. Cohen of Smith College implemented a modified Moore method for courses in Infinite-dimensional Linear Algebra and Real Analysis.
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.