Bayu Riyadhus Saputro, Sumaji
Abstract
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Lebesgue integral was defined constructively by using outer measure, measurable set, measurable function and Lebesgue measure concept. Then it was constructed by using simple function. The requirement of a Lebesgue integrable function to be Riemann integrable is bounded function and the set of discontinuities of that function has measure zero.
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Lebesgue integral was defined constructively by using outer measure, measurable set, measurable function and Lebesgue measure concept. Then it was constructed by using simple function. The requirement of a Lebesgue integrable function to be Riemann integrable is bounded function and the set of discontinuities of that function has measure zero.
Key concepts: Lebesgue–Stieltjes integration, Lebesgue integration, Locally integrable function, Riemann integral, Classification of discontinuities, Mathematics, Lebesgue measure, Measurable function