INTEGRAL PERRON DAN EKUIVALENSINYA DENGAN INTEGRAL DENJOY

Riva Yasin Nurandini, Encum Sumiaty, Cece Kustiawan

Abstract


ABSTRAK. Integral Perron adalah pengembangan dari integral Lebesgue, sehingga dengan menggunakan definisi integral Perron suatu fungsi yang tak terintegralkan Lebesgue dapat terintegralkan Perron. Sama halnya dengan integral Riemann dan integral Lebesgue, integral Perron juga memiliki sifat-sifat dasar integral diantaranya kelinearan, keterurutan, dan penambahan selang. Selain integral Perron, integral Denjoy juga merupakan pengembangan dari integral Lebesgue, hanya saja pendefinisian yang dilakukan oleh Denjoy berbeda dengan Perron. Oleh karena itu, pada penelitian ini akan dikaji hubungan antara integral Perron dan integral Denjoy, juga sifat-sifat yang dimiliki oleh integral Perron.

Kata Kunci : Fungsi Mayor, Fungsi Minor, Turunan Atas, Turunan Bawah, ACG*, Integral Perron, Integral Denjoy.

ABSTRACT.The Perron Integral is the development of the integral Lebesgue, by using Perron's integral definition an unintegrated function of Lebesgue can be integrated Perron. Similar to the Riemann integral and the Lebesgue integral, the Perron integral also has the integral basic properties such as linearity, obedience, and the addition of a line. In addition to the integral Perron, the integral Denjoy is also the development of the integral Lebesgue, but the definition of Denjoy is different from Perron. Therefore, in this study will examine the relationship between the Perron integral and Denjoy integral, also the properties possessed by the Perron integral.

Keyword : Major Function, Minor Function, Upper Derivative, Lower Derivative, ACG*, Perron Integral, Denjoy Integral.

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References


Bartle, R.G. dan Sherbert, D.R. (2000). Introduction to Real Analysis (third Ed). New York: John Wiley & Sons.

Bruckner, A.M., Fleissner, R.J., dan Foran, J. (1986). The Minimal Integral Which Includes Lebesgue Integrable Functions and Derivatives. California : Colloquium Mathematicum. Vol. L.

Gordon, R.A. (1994). Theory of the Lebesgue, Denjoy, Perron, and Henstock Integral. Rhode Island: AMS Publishing Company.

Hamzah, D.A. (2009). Integral Denjoy dan Keterkaitannya dengan Integral Henstock. Skripsi pada UPI Bandung.

Hu, S., dan Lakshmikantham. (1987). Some Remarks on Generalized Riemann Integral. Texas : Journal of Mathematical Analysis and Applications.

Malik, S.C., dan Arora, S. (1992). Mathematical Analysis. Delhi : John Wiley & Sons.

McShane, E.J. (1947). Integration. London : Princeton University Press.

Royden, H.L. (2000). Real Analysis (second Ed). London: The Macmillan Company.

Saks, S. (1937). Theory of the Integral. New York: Hafner Publishing Company.


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