Song Zhan
Abstract
The advantages of Lebesgue integral are explained. And Lebesgue controlling convergence is proved by Fatou theorem. It is indicated that three great theorems of Lebesgue inegral: Levi theorem, Fatou theorem and Lebesgue controlling couvergence, are of equal value and can constitute a circulation of proving one with another.
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The advantages of Lebesgue integral are explained. And Lebesgue controlling convergence is proved by Fatou theorem. It is indicated that three great theorems of Lebesgue inegral: Levi theorem, Fatou theorem and Lebesgue controlling couvergence, are of equal value and can constitute a circulation of proving one with another.
Key concepts: Lebesgue integration, Dominated convergence theorem, Lebesgue–Stieltjes integration, Lebesgue's number lemma, Mathematics, Riemann integral, Lp space, Pure mathematics