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    Real Analysis : Lebesgue Integral and Monotone Convergence Theorem

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    Let f be a nonnegative integrable function. Show that the function F defined by F(x)= Integral[from -inf to x of f] is continuous by using the Monotone Convergence Theorem.

    From Royden's Real Analysis Text, chapter 4.

    See the attached file.

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    Solution Summary

    Lebesgue Integrals and the Monotone Convergence Theorem are investigated in the solution.