ON THE CONVERGENCE THEOREMS OF THE McSHANE INTEGRAL FOR RIESZ-SPACES-VALUED FUNCTIONS DEFINED ON REAL LINE

Authors

  • Muslim Ansori Mathematics Departement, Universitas Lampung
  • Yosephus D. Sumanto Mathematics Departement, Universitas Diponegoro
  • Novi Rustiana Dewi Mathematics Dept. Universitas Sriwijaya, Palembang

DOI:

https://doi.org/10.21831/pg.v3i2.654

Abstract

This paper is a partial result  of our researchs  in the main topic "On The McShane Integral for Riesz-Spaces-valued Functions Defined on the space  ". We have constructed  McShane integral for Riesz-spaces-valued functions defined on  the space   by a technique involving double sequences and  proved some basic properties which coincides with the McShane Integral for Banach-spaces valued functions defined on real line. Further, we construct some convergence theorems involving uniformly convergence theorems, monotone convergence theorems and Fatou’s lemma in the sense of this integral.
Keywords : Riesz Space, McShane Integral

Additional Files

How to Cite

Ansori, M., Sumanto, Y. D., & Dewi, N. R. (2012). ON THE CONVERGENCE THEOREMS OF THE McSHANE INTEGRAL FOR RIESZ-SPACES-VALUED FUNCTIONS DEFINED ON REAL LINE. PYTHAGORAS Jurnal Matematika Dan Pendidikan Matematika, 3(2). https://doi.org/10.21831/pg.v3i2.654

Issue

Vol. 3 No. 2: Desember 2007

Section

Articles

License

Creative Commons License
Pythagoras is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://journal.uny.ac.id/index.php/pythagoras.