Kriteria Cauchy Integral Riemann di Ruang Riesz

Muhammad Arifin Ilham, Jerrico Nugroho, Made Tantrawan

Abstract


In 2008, Boccuto and Candeloro [4] introduced a variant of Riemann integral for Riesz valued functions defined on an order interval in a Riesz space. In this paper, we present an equivalent definition and several Cauchy criterion versions of the integral. Furthermore, some applications of the Cauchy criterion are provided.


Keywords


Integral Riemann; Kriteria Cauchy; Ruang Riesz

Full Text:

PDF

References


S.J. Ali and P. Mondal, “Riemann and Riemann-type Integration in Banach Spaces”, Real Analysis Exchange, vol 32, pp. 403-440, 2014.

C.D. Aliprantis and O. Burkinshaw, Locally solid Riesz spaces with applications to economics. American Mathematical Society, 2003.

R.G. Bartle and D.R. Sherbert, Introduction to Real Analysis 4th Edition, John Wiley & Sons, 2011.

A. Boccuto and D. Candeloro, “Integral and Differential Calculus in Riesz spaces and applications”, Functional Analysis and its Applications, vol. 3, pp. 89–111, 2008.

N.H.S. Haidar, “A Sobolev Space Inroad to Riemann Integrability”, Turkish Journal of Analysis and Number Theory, vol 8, pp. 34-38, 2020.

A. Kalauch and O.V. Gaans, Pre-Riesz Spaces. De Gruyter, 2019.

F.B. Liebrich and G. Svindland, “Model Spaces for Risk Measures”, Insurance: Mathematics and Economics, vol 77, pp. 150-165, 2017.

W.A.J. Luxemburg and A.C. Zaanen, Riesz Spaces I. North-Holland Publ. Co., 1971.

R.E. Maza and S.R. Canoy, Jr., “Denjoy-type Integrals in Locally Convex Topological Vector Space”, European Journal of Pure and Applied Mathematics, vol 14, pp. 1169-1183, 2021.

R.R. Reitano, Foundations of Quantitative Finance-Book III: The Integrals of Riemann, Lebesque, and (Riemann-)Stieltjes. CRC Press, 2023.

A. Torchinsky, A Modern View of the Riemann Integral, Springer, 2022.

A.C.M. van Rooij and W.B. van Zuijlen, “Integrals for Functions with Values in a Partially Ordered Vector Space”, Positivity, vol 20, pp. 877-916, 2016.

X. You, D. Zhao, and D.F.M. Torres, “On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales”, Journal of Nonlinear Sciences and Applications, vol 10, pp. 2487-2500, 2017.




DOI: http://dx.doi.org/10.12962/limits.v21i2.20482

Refbacks

  • There are currently no refbacks.


Jumlah Kunjungan:

Creative Commons License
Limits: Journal Mathematics and its Aplications by Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/limits.