Comprehensive analysis of product inequalities for Hewitt-Stromberg measures in separable metric spaces
*Rihab GuedriCorresponding authorrihab.guedri@fsm.rnu.tnDepartment of MathematicsFaculty of Sciences of MonastirUniversity of MonastirMonastir, 5000, TunisiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Nov 2024
- Published Online:
- 05 Mar 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2271
- Pages:
- 1771–1793
Abstract
Keywords
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References
[1] N. Attia, “Relative multifractal spectrum,” Commun. Korean Math. Soc, vol. 33, no. 2, pp. 459–471 (2022).
[2] N. Attia and R. Guedri, “A note on the Regularities of Hewitt-Stromberg h-measures,” Ann Univ Ferrara, vol. 69, no. 1, pp. 121-137 (2022).
[3] N. Attia, R. Guedri, and O. Guizani, “Note on the multifractal measures of cartesian product sets,” Commun. Korean Math. Soc, vol. 37, no. 4, pp. 1073-1097 (2022).
[4] N. Attia, H. Jebali, and R. Guedri, “On a class of Hausdorff measure of cartesian product sets in metric spaces,” Topol. Methods Nonlinear Anal, vol. 62, no. 2, pp. 601–623 (2023).
[5] N. Attia and B. Selmi, “Regularities of multifractal Hewitt-Stromberg measures,” Commun. Korean Math. Soc, vol. 34, no. 1, pp. 213-230 (2019).
[6] N. Attia, H. Jebali, and M. Ben Hadj Khlifa, “A note on fractal measures of cartesian product sets,” Bull. Malays. Math. Sci. Soc, vol. 44, no. 6, pp. 4383-4404 (2021).
[7] V. Çetkin, “Partial soft metric spaces: Convergence,” J. Interdiscip. Math, vol. 24, no. 4, pp. 881-892 (2022).
[8] Z. Douzi and B. Selmi, “Multifractal analysis of Hewitt-Stromberg measures with respect to gauge control functions,” Topol. Methods Nonlinear Anal, vol. 1, no. 1, pp. 1-43 (2024).
[9] P. Dhawan and A. Grewal, “B-multiplicative metric spaces : Coupled coincidence points with application,” J. Interdiscip. Math, vol. 27, no. 8, pp. 1909–1914 (2024).
[10] G. A. Edgar, “Centred densities and fractal measures,” New York J. Math, vol 13, no. 2, pp. 33-87 (2007).
[11] B. Esmayli and P. H. Lasz, “The Coarea inequality,” Ann. Fenn. Math, vol. 46, no. 2, pp. 965–991 (Aug. 2021).
[12] G. A. Edgar, “Fractal Measures,” Springer, New York (1998).
[13] G. A. Edgar, “Packing measure in general metric space,” Real Anal. Exchange, vol. 26, no. 2, pp. 831-852 (2001).
[14] K. J. Falconer, “Fractal Geometry: Mathematical Foundations and Applications,” John Wiley & Sons (2013).
[15] R. Guedri and N. Attia, “On the generalized Hausdorff and packing measures of product sets in metric space,” Math. Inequal. Appl, vol. 25, no. 2, pp. 335-358 (2022).
[16] A. Hewitt and K. Stromberg, “Real and Abstract Analysis. A modern treatment of the theory of functions of a real variable,” Springer-Verlag, New York (1965).
[17] J. D. Howroyd, “On Hausdorff and packing dimension of product spaces,” Math. Proc. Camb. Philos. Soc, vol. 119, no. 4, pp. 715-727 (1996).
[18] J. D. Howroyd, “On the theory of Hausdorff measure in metric spaces,” University of London, University College London, UK (1995).
[19] X. Hu and S. J. Taylor, “Fractal properties of products and projections of measures in Rd,” Math. Proc. Camb. Phil. Soc, vol. 115, no. 3, pp. 527-544 (1994).
[20] H. Joyce and D. Preiss, “On the existence of subsets of positive finite packing measure,” Mathematika, vol. 42, no. 1, pp. 14-24 (1995).
[21] J. D. Kelly, “A method for constructing measures appropriate for the study of Cartesian products,” Proc. London Math. Soc, vol. 26, no. 3, pp. 521-546 (1973).
[22] L. Olsen, “A multifractal formalism,” Advances in Mathematics, vol. 116, vol. 1, pp. 82-196 (1995).
[23] L. Olsen, “Multifractal dimensions of product measures,” Math. Proc. Camb. Phil. Soc, vol. 120, no. 4, pp. 709-743 (1996).
[24] Y. Pesin, “Dimension theory in dynamical systems: contemporary views and applications,” University of Chicago Press (1997).
[25] X. S. Raymond and C. Tricot, “Packing regularity of sets in n-space,” Math. Proc. Camb. Philos. Soc, vol. 103, no. 1, pp. 133-145 (1988).
[26] B. Selmi, “A review on multifractal analysis of Hewitt-Sromberg measures,” J Geom Anal, vol. 32, no. 1, pp. 12 (2022).
[27] B. Selmi, “On the multifractal dimensions of product measures,” NS, vol. 29, no. 1 (Feb. 2022).
[28] B. Selmi, “The relative multifractal densities: a review and application,” J. Interdiscip. Math, vol. 24, no. 6, pp. 1627-1644 (2021).
[29] B. S. Thomson, “Construction of measures in metric spaces,” J. London Math. Soc, vol. 2, no. 1, pp. 21-24 (1976).
[30] S. Wen and M. Wu, “Relations between packing premeasure and measure on metric space,” Acta Math Sci, vol. 27, no. 1, pp. 137-144 (2007).
[31] O. Zindulka, “Packing measures and dimensions on Cartesian products,” Publ. Mat, vol. 57, no. 2, pp. 393-420 (2013).
