SIFAT-SIFAT DASAR INTEGRAL HENSTOCK
Keywords:
Henstock Integral, Partitions, Riemann Integral, ï¤-Positive Constant
Abstract
This paper was a review about theory of Henstock integral. Riemann gave a definition of integral based on the sum of the partitions in Integration area (interval [a, b]). Those
partitions is a ï¤ -positive constant. Independently, Henstock and Kurzweil replaces ï¤- positive constant on construction Riemann integral into a positive function, ie ï¤(x)>0 for
every x[a, b]. This function is a partition in interval [a, b]. From this partitions, we can defined a new integral called Henstock integral. Henstock integral is referred to as a
complete Riemann integral, because the basic properties of the Henstock integral is more constructive than Riemann Integral.
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References
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Thobirin, A. (1997). Beberapa Integral Jenis Riemann. Tesis Magister pada Jurusan Matematika FMIPA Universitas Gadjah Mada, Yogyakarta.
Gordon, R. A., (1994), The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Graduate Studies in Mathematics 4, American Mathematical Society, Providence.
Guoju, Y. & Tianqing, A., (1998), On Henstock-Dunford and Henstock Pettis Integral, 12 hlm, Hindawi Publishing Corp, http://ijmms.hindawi.com. 08 Januari 2005, Pk. 17.00 WIT
Lee, P. Y., (1989), Lanzhou Lectures on Henstock Integration, Series in Real Analysis vol. 2, World Scientific, Singapore.
Royden, H. L., (1987), Real Analysis, Third Edition, Macmillan Publishing Company, New York.
Rudin, W., (1976), Principles of Mathematical Analysis, Third Edition, Mc Graw-Hill Kogakusha. Ltd, Tokyo.
Schecter, E. (2001). An Introduction to The Gauge Integral. 10 hlm. http://www.math.vanderbilt.edu/~schectex/ccc/. 08 Januari 2005, pk. 18.47 WIT.
Sinay, L. J. (2005) , Integral Henstock dan Sifat-Sifatnya, Skripsi S1 pada Jurusan Matematika FMIPA Universitas Pattimura, Ambon.
Soemantri, R., (1988), Analisis Real I, Penerbit Karunika, Universitas Terbuka, Jakarta.
Thobirin, A. (1997). Beberapa Integral Jenis Riemann. Tesis Magister pada Jurusan Matematika FMIPA Universitas Gadjah Mada, Yogyakarta.
Published
2012-12-02
How to Cite
[1]
L. Sinay, “SIFAT-SIFAT DASAR INTEGRAL HENSTOCK”, BAREKENG: J. Math. & App., vol. 6, no. 2, pp. 7-15, Dec. 2012.
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