SIFAT-SIFAT INTEGRAL RIEMANN-STIELTJES - Rumlawang, Francis Y.; Batkunde, Harimanus (BAREKENG: Jurnal Ilmu Matematika dan Terapan, 2007)
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