TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

An analytical innovation from foundations to modern applications of advancing measure theory via approach structure

* , ,

* Corresponding author · click or hover a name for details

pp. 363–370Vol. 29Issue 2February 2026DOI: 10.47974/JIM-2191XML
Received:
06 Nov 2024
Published Online:
13 Feb 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2191
Pages:
363–370

Abstract

In this research, we define and prove various features of a new measure based on the idea of approach structure, known as the approach measure. We then discuss the relationship between the new and traditional measures. We introduce another new notion, the semi-approach measure, and investigate the relation between these two concepts.

Keywords

Subject Classifications

28A3346E27

References

[1] S.J. Taylor, “Introduction to measure and integration”, Cambridge University press (1966). 
[2] R. Dalang, A. Morton and W. Willinger, Equivalent Martingale Measures and No-Arbitrage in Stochastic Securities Market Models. Stochastics and Stochastic Reports, vol 29, pp. 185-201 (1990).
https://doi.org/10.1080/17442509008833613.
[3] R. Baekeland and R. Lowen, “Measures of Lindelöf and separability in approach spaces.,” Int. J. Math. Math. Sci, vol. 17, no. 3, pp. 597-606 (1994). https://eudml.org/doc/47159.
[4] B.Y. Hussein, On Equivalent martingale measure, Ph.D. thesis University of Al-Mustnsiryah (2007).
[5] B.Y. Hussein, Equivalent locally Martingale Measure for the deflator process on ordered Banach algebra, J. Math. vol. 2020, pp. 1-7 (2020), https://doi.org/10.1155/2020/5785098.
[6] R.K. Abbas and B.Y. Hussein, New Results of Normed Approach Space, Iraqi J. Sci., Vol. 63, No. 5, pp. 2103-2113 (2022). https://doi.org/10.24996/ijs.2022.63.5.25.
[7] R.K. Abbas and B.Y. Hussein, New Results of CompAssume thation Normed Approach Space, AIP conf. Proc. Of the 2rd International Scientific conferences of Pure Scinences, University of Al-Qadisiyah, (2021).
[8] R.K. Abbas and B.Y. Hussein, “A new kind of topological vector space: Topological approach vector space,” AIP conference proceedings, vol. 2386, pp. 060008-060008 (2022). https://doi.org/10.1063/5.0066971.
[9] B.Y. Hussein and S.S. Abd, On New Results of Normed Approach Space Via β-Approach structure, Iraqi J. Sci., Vol. 63, No. 5, pp. 3538-3550 (2022). https://doi.org/10.24996/ijs.2023.64.7.33
[10] B.Y. Hussein and H.A.A. Wshayeh, “On state space of measurable function in symmetric Δ-Banach algebra with new results,” AIP Conference Proceedings, vol. 2398, p. 060064-060075 (2022), https://doi.org/10.1063/5.0093486.
[11] M.A.A. Neamah and B.Y. Hussein, Some New Results of CompAssume thation tw Normed Approach Space, Periodicals of Engineering and natural Sciences, vol. 10, no. 5, pp. 82-89 (2022).
[12] M.A.A. Neamah and B.Y. Hussein, New Type of topological vector space Via tw-Approach Structure, J. Algaebraic Statistics, vol. 13, no. 3, pp. 2714-2724 (2022), https://publishoa.com/index.php/journal/article/view/935.
[13] D.A. Kadhim and B.Y. Hussein, New kind of Banach Algebra Via Proximit structure,” Wasit Journal for Pure Sciences, vol. 2, no. 2, pp. 23-37 (2023), https://doi.org/10.31185/wjps.95.
[14] D.A. Kadhim, B.Y. Hussein, “A new kind of topological vector space via proximit structure,” J. Interdiscip. Math., vol. 26, no. 6, pp. 1065-1075 (2023), https://doi.org/10.47974/jim-1606.
[15] S.M. Kadham and M.A. Mustafa, “Medical applications of the new-transform,” J. Interdiscip. Math., vol. 26, no. 6, pp. 1341-1353 (2023), https://doi.org/10.47974/jim-1632
[16] A.S. Maani, H.K. Alkhayyat and S.M. Kadham. “Enhance MRI images of lung cancer using hybrid transform,” J. Discrete Math. Sci. Cryptography, vol. 26, no. 7, pp. 1897-1902 (2023), https://doi.org/10.47974/jdmsc-1682.
[17] B.A. Hassan and A.A. Saad, “Elastic conjugate gradient methods to solve iteration problems,” J. Interdiscip. Math., vol. 26, no. 6 (2023). https://doi.org/10.47974/JIM-1619.
[18] B.A. Hassan, H.N. Jabbar and Y.A. Laylani, “Upscaling parameters for conjugate gradient method in unconstrained optimization,” J. Interdiscip. Math., vol. 26, no. 6 (2023). https://doi.org/10.47974/JIM-1615.
[19] B.A. Hassan and A.A. Saad, “Explaining new parameters conjugate analysis based on the quadratic model,” J. Interdiscip. Math., vol. 26, no. 6 (2023). https://doi.org/10.47974/JIM-1620.
[20] A.H. Alwan, “Small intersection graph of subsemimodules of a semimodule,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2022, no. 1, pp. 15-22 (2022). 
[21] S. Ediz, M. Cancan and M.R. Farahani, “Eccentric connectivity and connective eccentricity indices of generalized Petersen graphs,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2021, no. 1, pp. 1-6 (2021). 
[22] R.B. Ash, Real analysis and probability, Academic process, NewYork (1992).
[23] R.B. Ash and C.A. Doleans-Dade, Probabilty and Measure Theory, Second Edition, with contributions from Catherine Doleans-Dade (1999).

 

Views: 100Downloads: 67Citations: 0