Lebesgue married the sister of one of his fellow students, and he and his wife had two children, Suzanne and Jacques.
Lebesgue once wrote, "Réduites à des théories générales, les mathématiques seraient une belle forme sans contenu." ("Reduced to general theories, mathematics would be a beautiful form without content.")
In measure-theoretic analysis and related branches of mathematics, the Lebesgue–Stieltjes integral generalizes Riemann–Stieltjes and Lebesgue integration, preserving the many advantages of the latter in a more general measure-theoretic framework.
Lebesgue integration has the property that every function defined over a bounded interval with a Riemann integral also has a Lebesgue integral, and for those functions the two integrals agree. Furthermore, every bounded function on a closed bounded interval has a Lebesgue integral and there are many functions with a Lebesgue integral that have no Riemann integral.