[1] N. Attia, “Relative multifractal spectrum,” J. Korean Math. Soc., vol. 33, pp. 459–471 (2018). [Online]. Available: https://www.koreascience.or.kr/article/JAKO201814442073436 doi: 10.4134/CKMS.c170143
[2] N. Attia and B. Selmi, “On the Billingsley dimension of Birkhoff average in the countable symbolic space,” Comptes Rendus Mathématique, vol. 358, no. 8, pp. 255–265 (2020). [Online]. Available: https://comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_8_939_0/ doi: 10.5802/crmath.21
[3] N. Attia and B. Selmi, “Relative multifractal box-dimensions,” Filomat, vol. 33, pp. 2841–2859 (2019). [Online]. Available: http://www.doiserbia.nb.rs/Article.aspx?ID=0354-51801909841Adoi: 10.2298/FIL1909841A
[4] N. Attia, B. Selmi, and C. Souissi, “Some density results of relative multifractal analysis,” Chaos, Solitons & Fractals, vol. 103, pp. 1–11 (2017). [Online]. Available: https://www.sciencedirect.com/science/article/abs/pii/S0960077917302242 doi: 10.1016/j.chaos.2017.05.029
[5] L. Barreira and J. Schmeling, “Sets of non-typical points have full topological entropy and full Hausdorff dimension,” Israel J. Math., vol. 116, pp. 29–70 (2000). [Online]. Available: https://link.springer.com/article/10.1007/BF02773211 doi: 10.1007/BF02773211
[6] A. Ben Mabrouk and B. Selmi, “On the topological Billingsley dimension of self-similar Sierpiński carpet,” Eur. Phys. J. Spec. Top., vol. 230, pp. 3861–3871 (2021). [Online]. Available: https://link.springer.com/article/10.1140/epjs/s11734-021-00313-8 doi: 10.1140/epjs/s11734-021-00313-8
[7] F. Ben Nasr, I. Bhouri, and Y. Heurteaux, “The validity of the multifractal formalism: results and examples,” Adv. Math., vol. 165, pp. 264–284 (2002). [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0001870801920250 doi: 10.1006/aima.2001.2025
[8] P. Billingsley, Convergence of Probability Measures, 2nd ed., Wiley Series in Probability and Statistics. New York: John Wiley & Sons (1999). [Online]. Available: https://onlinelibrary.wiley.com/doi/book/10.1002/9780470316962 ISBN: 9780471197454
[9] P. Billingsley, Ergodic Theory and Information. New York: Wiley (1965). [Online]. Available: https://www.amazon.com/Ergodic-Information-Probability-Mathematical-Statistics/dp/0471072508 ISBN: 978-0471072508
[10] H. Cajar, Billingsley Dimension in Probability Spaces, Lecture Notes in Mathematics, vol. 892. New York: Springer (1981). [Online]. Available: https://mathscinet.ams.org/mathscinet-getitem?mr=0654147 ISBN: 3-540-11164-6
[11] J. Cole, “Relative multifractal analysis,” Chaos, Solitons & Fractals, vol. 11, pp. 2233–2250 (2000). [Online]. Available: https://www.sciencedirect.com/science/article/abs/pii/S0960077999001435 doi: 10.1016/S0960-0779(99)00143-5
[12] M. Das, “Local properties of self-similar measures,” Illinois J. Math., vol. 42, no. 2, pp. 313–332 (1998). [Online]. Available: https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-42/issue-2/Local-properties-of-self-similar-measures/10.1215/ijm/1256045047.full doi: 10.1215/ijm/1256045047
[13] Z. Douzi and B. Selmi, “A relative multifractal analysis: box-dimensions, densities, and projections,” Quaest. Math., vol. 45, no. 1, pp. 1–54 (2022). [Online]. Available: https://www.tandfonline.com/doi/abs/10.2989/16073606.2021.1941375 doi: 10.2989/16073606.2021.1941375
[14] Z. Douzi, B. Selmi, and A. Ben Mabrouk, “The refined multifractal formalism of some homogeneous Moran measures,” Eur. Phys. J. Spec. Top., vol. 230, pp. 3815–3834 (2021). [Online]. Available: https://ui.adsabs.harvard.edu/abs/2021EPJST.230.3815D doi: 10.1140/epjs/s11734-021-00318-3
[15] Z. Douzi, B. Selmi, and H. Zyoudi, “The measurability of Hewitt-Stromberg measures and dimensions,” Commun. Korean Math. Soc., vol. 38, no. 2, pp. 491–507 (2023). [Online]. Available: https://ckms.kms.or.kr/journal/view.html?uid=2586 doi: 10.4134/CKMS.c220154
[16] Z. Douzi and B. Selmi, “Multifractal variation for projections of measures,” Chaos, Solitons & Fractals, vol. 91, pp. 414–420 (2016). [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0960077916302223 doi: 10.1016/j.chaos.2016.06.026
[17] Z. Douzi and B. Selmi, “The mutual singularity of the relative multifractal measures,” Nonauton. Dyn. Syst., vol. 8, no. 1, pp. 18–26 (2021). [Online]. Available: https://www.degruyter.com/document/doi/10.1515/msds-2020-0123/html doi: 10.1515/msds-2020-0123
[18] K. J. Falconer, Fractal Geometry: Mathematical Foundations and Applications, 1st ed. Chichester: Wiley (1990). [Online]. Available: https://www.maa.org/press/maa-reviews/fractal-geometry-mathematical-foundations-and-applications ISBN: 9781119942399
[19] L. Guo, B. Selmi, Z. Li, and H. Zyoudi, “Probabilistic spaces and generalized dimensions: A multifractal approach,” Chaos, Solitons & Fractals, vol. 192, 115953 (2025). [Online]. Available: https://www.sciencedirect.com/science/article/abs/pii/S0960077924015054 doi: 10.1016/j.chaos.2024.115953
[20] T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, “Fractal measures and their singularities: The characterization of strange sets,” Phys. Rev. A, vol. 33, no. 2, pp. 1141–1151 (1986). [Online]. Available: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.33.1141 doi: 10.1103/PhysRevA.33.1141
[21] A. S. Kechris, Classical Descriptive Set Theory, Graduate Texts in Mathematics, vol. 156. New York: Springer-Verlag (1994). [Online]. Available: https://link.springer.com/book/10.1007/978-1-4612-4190-4 ISBN: 978-1-4612-8692-9
[22] M. Khelifi, H. Lotfi, A. Samti, and B. Selmi, “A relative multifractal analysis,” Chaos, Solitons & Fractals, vol. 140, 110091 (2020). [Online]. Available: https://www.sciencedirect.com/science/article/abs/pii/S0960077920304884 doi: 10.1016/j.chaos.2020.110091
[23] K. Kuratowski, Topology, Volume II. New York: Academic Press (1968). [Online]. Available: https://www.vitalsource.com/products/topology-k-kuratowski-v9781483271798 ISBN: 9781483271798
[24] J. Lévy Véhel and R. Vojak, “Multifractal analysis of Choquet capacities,” Adv. Appl. Math., vol. 20, no. 1, pp. 1–43 (1998). [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0196885896905175 doi: 10.1006/aama.1996.0517
[25] Z. Li and B. Selmi, “On the multifractal analysis of measures in a probability space,” Illinois J. Math., vol. 65, no. 3, pp. 687–718 (2021). [Online]. Available: https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-65/issue-3/On-the-multifractal-analysis-of-measures-in-a-probability-space/10.1215/00192082-9446058.short doi: 10.1215/00192082-9446058
[26] Z. Lin and H. Wang, Weak Convergence and Its Applications. Singapore: World Scientific (2014). [Online]. Available: https://www.perlego.com/book/851222/weak-convergence-and-its-applications-pdf ISBN: 9789814447713
[27] B. B. Mandelbrot, Les Objets fractals: forme, hasard et dimension. Paris: Flammarion (1975). [Online]. Available: https://www.abebooks.com/9782082106474/objets-fractals-Forme-hasard-dimension-2082106470/plp ISBN: 9782082106474
[28] B. B. Mandelbrot, The Fractal Geometry of Nature. San Francisco: W. H. Freeman (1982). [Online]. Available: https://www.bookdepository.com/Fractal-Geometry-Nature-Benoit-B-Mandelbrot/9780716711865 ISBN: 9780716711865
[29] P. Mattila, “Integralgeometric properties of capacities,” Trans. Amer. Math. Soc., vol. 266, no. 2, pp. 539–554 (1981). [Online]. Available: https://www.ams.org/journals/tran/1981-266-02/S0002-9947-1981-0617550-8/doi:10.1090/S0002-9947-1981-0617550-8
[30] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, Cambridge Studies in Advanced Mathematics, vol. 44. Cambridge: Cambridge University Press (1995). [Online]. Available: https://opac.lib.shizuoka.ac.jp/opac/en/recordID/catalog.bib/BA24492071 ISBN: 9780521465762
[31] P. Mattila and R. D. Mauldin, “Measures and dimension functions: Measurability and densities,” Math. Proc. Cambridge Philos. Soc., vol. 121, no. 1, pp. 81–100 (1997). [Online]. Available: https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/abs/measures-and-dimension-functions-measurability-and-densities/113238E646E8668B81A01E3F9624F43C doi: 10.1017/S0305004196001089
[32] L. Olsen, “A multifractal formalism,” Adv. Math., vol. 116, no. 1, pp. 82–196 (1995). [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0001870885710663 doi: 10.1006/aima.1995.1066
[33] L. Olsen, “Measurability of multifractal measure functions and multifractal dimension functions,” Hiroshima Math. J., vol. 29, no. 3, pp. 435–458 (1999). [Online]. Available: https://projecteuclid.org/journals/hiroshima-mathematical-journal/volume-29/issue-3/Measurability-of-multifractal-measure-functions-and-multifractal-dimension-functions/10.32917/hmj/1206124851.full doi: 10.32917/hmj/1206124851
[34] L. Olsen, “Multifractal geometry,” in Fractal Geometry and Stochastics II, Progress in Probability, vol. 46, Birkhäuser, Basel, pp. 3–37 (2000). [Online]. Available: https://link.springer.com/chapter/10.1007/978-3-0348-8380-1_1 doi: 10.1007/978-3-0348-8380-1_1
[35] L. Olsen, “Self-affine multifractal Sierpiński sponges in Rd,” Pac. J. Math., vol. 183, no. 1, pp. 143–199 (1998). [Online]. Available: https://msp.org/pjm/1998/183-1/p07.xhtml doi: 10.2140/pjm.1998.183.143
[36] X. Peng, W. Li, and M. Dai, “Relative multifractal analysis in a probability space,” Int. J. Nonlinear Sci., vol. 10, no. 3, pp. 313–319 (2010).
[37] Y. Pesin, “Generalized spectrum for the dimension: the approach based on Carathéodory’s construction,” in Constantin Carathéodory: An International Tribute, vol. 3, World Sci. Publishing, Teaneck, NJ, pp. 1108–1119 (1991). [Online]. Available: https://www.worldscientific.com/doi/abs/10.1142/9789814350921_0055 doi: 10.1142/9789814350921_0055
[38] J. Peyrière, “Multifractal measures,” in Probabilistic and Stochastic Methods in Analysis with Applications (NATO ASI Series C: Mathematical and Physical Sciences, vol. 372), Il Ciocco, pp. 175–186 (1992). Dordrecht: Kluwer Academic Publishers. [Online]. Available: https://link.springer.com/chapter/10.1007/978-94-011-2791-2_7 doi: 10.1007/978-94-011-2791-2_7
[39] X. S. Raymond and C. Tricot, “Packing regularity of sets in n-space,” Math. Proc. Cambridge Philos. Soc., vol. 103, pp. 133–145 (1988). [Online]. Available: https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/abs/packing-regularity-of-sets-in-nspace/9CFA3A137FF118564E44BA1F7F031D2A doi: 10.1017/S0305004100064690
[40] R. Riedi and I. Scheuring, “Conditional and relative multifractal spectra,” Fractals, vol. 5, no. 2, pp. 153–168 (1997). [Online]. Available: https://www.worldscientific.com/doi/abs/10.1142/S0218348X97000152 doi: 10.1142/S0218348X97000152
[41] C. A. Rogers, Hausdorff Measures. Cambridge: Cambridge University Press (1970). [Online]. Available: https://www.bookdepository.com/Hausdorff-Measures-C-Rogers/9780521624916 ISBN: 9780521624916
[42] B. Selmi and H. Zyoudi, “Regarding the set-theoretic complexity of the general fractal dimensions and measures maps,” Analysis (Berlin) (2024). [Online]. Available: https://www.degruyter.com/document/doi/10.1515/anly-2024-0087/html doi: 10.1515/anly-2024-0087
[43] B. Selmi and H. Zyoudi, “The smoothness of multifractal Hewitt-Stromberg and box dimensions,” J. Nonlinear Funct. Anal., vol. 2024, art. 11 (2024). [Online]. Available: https://jnfa.mathres.org/archives/3259 doi: 10.23952/jnfa.2024.11
[44] B. Selmi, “Measure of relative multifractal exact dimensions,” Adv. Appl. Math. Sci., vol. 17, pp. 629–643 (2018).
[45] B. Selmi, “Multifractal dimensions for projections of measures,” Bol. Soc. Paran. Mat. (2018). [Online]. Available: https://arxiv.org/abs/1806.04636 (arXiv:1806.04636)
[46] B. Selmi, “On the strong regularity with the multifractal measures in a probability space,” Anal. Math. Phys., vol. 9, pp. 1525–1534 (2019). [Online]. Available: https://link.springer.com/article/10.1007/s13324-018-0261-5 doi: 10.1007/s13324-018-0261-5
[47] B. Selmi, “The relative multifractal analysis, review and examples,” Acta Sci. Math. (Szeged), vol. 86, pp. 635–666 (2020). [Online]. Available: https://link.springer.com/content/pdf/10.14232/actasm-020-801-8.pdf doi: 10.14232/actasm-020-801-8
[48] B. Selmi, “The relative multifractal densities: a review and application,” J. Interdiscip. Math., vol. 24, no. 6, pp. 1627–1644 (2021). [Online]. Available: https://www.tandfonline.com/doi/abs/10.1080/09720502.2020.1860286 doi: 10.1080/09720502.2020.1860286
[49] S. J. Taylor and C. Tricot, “Packing measure, and its evaluation for a Brownian path,” Trans. Amer. Math. Soc., vol. 288, no. 2, pp. 679–699 (1985). [Online]. Available: https://www.ams.org/journals/tran/1985-288-02/S0002-9947-1985-0776398-8/ doi:10.1090/S0002-9947-1985-0776398-8
[50] C. Tricot, “Two definitions of fractional dimension,” Math. Proc. Cambridge Philos. Soc., vol. 91, no. 1, pp. 57–74 (1982). [Online]. Available: https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/abs/two-definitions-of-fractional-dimension/06084FBF2CDE818DEEC1389E107D0D36 doi: 10.1017/S0305004100059119