Name for LDC: Lebesgue?

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Is there also a name associated to the Lebesgue dominated convergence theorem like Beppo-Levi or Fatou? Would Lebesgue be reasonable? Who did originally prove it?

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The result is due to Lebesgue. Bogachev (Measure Theory, Volume 1, Springer, page 428) writes:

"The Lebesgue dominated convergence theorem in the general case (with an integegrable majorant) was given by him [Lebesgue] [...]"

The specific reference that is given is (the link leads to a free copy):

H. Lebesgue, Sur la méthode de M. Goursat pour la résolution de l'équation de Fredholm, Bulletin de la Société Mathématique de France, 36 (1908), 3-19.