Integral Riemann-Stieltjes Dengan Batas-Batas Integrasi Fungsi Kontinu

Alifuddin, Moch. (2025) Integral Riemann-Stieltjes Dengan Batas-Batas Integrasi Fungsi Kontinu. Masters thesis, Institut Teknologi Sepuluh Nopember.

Text 6002222001-Master_Thesis.pdf - Accepted Version Restricted to Repository staff only until 1 April 2027. Download (1MB) | Request a copy

Abstract

Integral Riemann-Stieltjes merupakan generalisasi dari Integral Riemann. Dalam tesis ini didefinisikan limit dan derivatif pada himpunan semua fungsi kontinu pada [a, b] dan Integral Riemann dengan batas integrasi fungsi-fungsi kontinu. Selanjutnya melalui Teorema Fundamental Kalkulus dibuktikan bahwa operator derivatif dan Integral Riemann saling invers. Kemudian didefinisikan generalisasi dari limit dan derivatif pada himpunan semua fungsi kontinu pada [a, b] serta didefinisikan Integral Riemann dengan batas integrasi fungsi kontinu pada [a, b] yang disebut limit Stieltjes,derivatif Stieltjes dan Integral Riemann-Stieltjes dengan batas fungsi kontinu dan menguraikan sifat-sifatnya. Selanjutnya melalui Teorema Fundamental Kalkulus dibuktikan bahwa operator derivatif Stieltjes dan Integral Riemann-Stieltjes saling invers. Hasil dari tesis ini berupa definisi dan sifat-sifat integral Riemann-Stieltjes dengan batas-batas integrasi fungsi kontinu.
===================================================================================================================================
Riemann-Stieltjes integral is generalization of Riemann integral.In this thesis we will define limit and derivative on the set of all continuous functions on [a, b], as well as the Riemann integral with limit of integration that are continuous functions. Further more through the Fundamental Theorem of Calculus,it is proven that derivative operator and Riemann integral operator are inverses of each other.Next, a generalization of limit and derivative on the set of all continuous functions on [a, b] is introduced, along with the Riemann integral with limit of integration that are continuous functions. This is referred to as Stieltjeslimit,Stieltjes derivative,and Riemann-Stieltjes integral with continuous function bounds.Their properties are also elaborated. Finally,through the Fundamental Theorem of Calculus, it is proven that Stieltjes derivative operator and the Riemann-Stieltjes integral are inverses of each other. The results of this thesis include definitions and properties of the Riemann-Stieltjes integral with limit of integration that are continuous functions.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Limit Stieltjes, Derivatif Stieltjes, Integral Riemann-Stieltjes
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA159 Algebra Q Science > QA Mathematics > QA322.2 Normed linear spaces. Banach spaces
Divisions:	Faculty of Mathematics, Computation, and Data Science > Mathematics > 44101-(S2) Master Thesis
Depositing User:	Moch. Alifuddin
Date Deposited:	03 Feb 2025 04:21
Last Modified:	03 Feb 2025 04:21
URI:	http://repository.its.ac.id/id/eprint/117869

Actions (login required)

View Item