SIFAT-SIFAT INTEGRAL RIEMANN-STIELTJES
Keywords:
Rieman-Stieltjes, Riemann-Stieltjes Integral
Abstract
If is limited and []ℜ→baf,:[]ℜ→ba,:α Monotone increase in [, is Riemann-Stieltjes integral able to α on ] ba,[]ba, simply written by[]αRSf∈ if . With JI=()()xdxfIbaα∫= is called Riemann Stieltjes lower integral f to α and ()()xdxfJbaα∫= is called Riemann Stieltjes upper integral f to α. Then is called Riemann Stieltjes upper integral f to ()()∫==baxdxfJIαα on [. if f ang g is Riemann Stieltjes integralable, and, k oe √ then f + g, kf, and fg is also Riemann Stieltjes integralable. But if f and ] ba,α have united discontinue point then f is not Riemann Stieltjes integralable on α
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References
Bartle, R. G., (1994), Introduction to Real Analysis, John Wiley & Sons, USA
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Gordon, R, A., (1994), The Integrals Of Lebesgue, Denjoy, Perron, and Henstock., Graduate Studies In Mathematics 4, Volume 4., American Mathematical Society,USA.
Hutahaean, E., (1989), Analisis Real II, Penerbit Karunika, Universitas Terbuka, Jakarta
Hutahaean, Leithold., (1986), Kalkulus dan Ilmu Ukur Analitik, edisi kelima jilid 1. Erlangga, Jakarta.
Jain, P. K. and Gupta, V. P., (1986), Lebesgue Measure and Integration. Wiley Eastern Limited, New Delhi.
Muslich., (2005), Analisis Real II, Lembaga Pengembangan Pendidikan,Surakarta.
Purcell, Edwin J, Varberg, Rigdon., (2003). Kalkulus, edisi kedelapan jilid 1. Erlangga, Jakarta. Royden, H, L., (1989), Real Analysis, Third Edition, Macmillan Publishing Company, New York. Soeparna, D., (2006), Pengantar Analisis Real, Universitas Gajah Mada, Yogyakarta. Soeparna, D., (2006), Pengantar Analisis Abstrak, Universitas Gajah Mada, Yogyakarta.
Soemantri, R., (1988), Analisis Real I, Karunia, Jakarta.
Published
2018-01-20
How to Cite
[1]
F. Rumlawang and H. Batkunde, “SIFAT-SIFAT INTEGRAL RIEMANN-STIELTJES”, BAREKENG, vol. 1, no. 2, pp. 25-30, Jan. 2018.
Section
Articles
