LEBESGUE’S CRITERION FOR INTEGRABILITY | Zendy

Bayu Riyadhus Saputro | Zendy; Sumaji | Zendy

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LEBESGUE’S CRITERION FOR INTEGRABILITY

Author(s) -

Bayu Riyadhus Saputro,

Sumaji

Publication year - 2018

Publication title -

edupedia

Language(s) - English

Resource type - Journals

eISSN - 2614-4409

pISSN - 2614-1434

DOI - 10.24269/ed.v2i1.85

Subject(s) - lebesgue–stieltjes integration , lebesgue integration , locally integrable function , riemann integral , classification of discontinuities , mathematics , lebesgue measure , measurable function , measure (data warehouse) , lebesgue's number lemma , null set , integrable system , pure mathematics , function (biology) , bounded function , riemann–stieltjes integral , mathematical analysis , bounded variation , set (abstract data type) , integral equation , computer science , singular integral , database , evolutionary biology , biology , programming language

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. Keyword: Riemann Integral, Lebesgue Integral, Measure Abstrak Integral Lebesgue didefinisikan secara konstruktif dengan memanfaatkan konsep ukuran luar, himpunan terukur, fungsi terukur dan ukuran Lebesgue. Selanjutnya, digunakan fungsi sederhana untuk membangun integral Lebesgue. Syarat suatu fungsi yang terintegral Lebesgue agar terintegral Riemann adalah fungsi tersebut terbatas dan himpunan titik-titik yang mengakibatkan fungsi tersebut tidak kontinu berukuran nol Kata Kunci: IntegralRiemann, Integral Lebesgue, Ukuran. How To Cite: Bayu Riyadhus Saputro (2018). Kriteria Lebesgue untuk Keterintegralan. Penerbitan Artikel Ilmiah Mahasiswa Universitas Muhammadiyah Ponorogo. 2(1): 12-21 © 2018 Universitas Muhammadiyah Ponorogo. All rights reserved ISSN 2614-1434 (Print) ISSN 2614-4409 (Online) PENERBITAN ARTIKEL ILMIAH MAHASISWA Universitas Muhammadiyah Ponorogo Jurmas: Jurnal Mahasiswa Universitas Muhammadiyah Ponorogo 2(1)(2018): 12-21 13

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