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the problem of integration in its historical context, addressing Augustin-Louis Cauchy, Peter Gustav Lejeune Dirichlet, and Bernhard Riemann. Lebesgue presents six conditions which it is desirable that the integral should satisfy, the last of which is "If the sequence f_n(x) increases to the limit f(x), the integral of f_n(x) tends to the integral of f(x)." Lebesgue shows that his

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