1 |
N. Attia and B. Selmi, Relative multifractal box-dimensions, Filomat 33 (2019), 2841-2859.
DOI
|
2 |
N. Attia and B. Selmi. Regularities of multifractal Hewitt-Stromberg measures, Commun. Korean Math. Soc. 34 (2019), 213-230.
DOI
|
3 |
N. Attia and B. Selmi, A multifractal formalism for Hewitt-Stromberg measures, Journal of Geometric Analysis, (to appear). https://doi.org/10.1007/s12220-019-00302-3
|
4 |
N. Attia and B. Selmi, On the multifractal analysis of Birkhoff sums on a non-compact symbolic space, Comptes rendus Mathematique., (to appear).
|
5 |
P. Billingsley, Hausdorff dimension in probability theory I, Illinois. J. Math. 4 (1960), 187-209.
DOI
|
6 |
P. Billingsley, Hausdorff dimension in probability theory II, Illinois. J. Math. 5 (1961), 291-298.
DOI
|
7 |
J. Cole, Relative multifractal analysis, Choas, Solitons & Fractals. 11 (2000), 2233-2250.
DOI
|
8 |
C. Dai and S.J. Taylor, Defining fractal in a probability space, Illinois. J. Math. 38 (1994), 480-500.
DOI
|
9 |
C. Dai, Frostman lemma for Hausdorff measure and Packing measure in probability spaces, J Nanjing University, Mathematical Biquarterly 12 (1995), 191-203.
|
10 |
C. Dai and Y. Hou, Frostman lemmas for Hausdorff measure and packing measure in a product probability space and their physical application, Chaos, Solitons and Fractals 24 (2005), 733-744.
DOI
|
11 |
C. Dai and Y. Li, A multifractal formalism in a probability space, Chaos, Solitons and Fractals 27 (2006), 57-73.
DOI
|
12 |
C. Dai and Y. Li, Multifractal dimension inequalities in a probability space, Chaos, Solitons and Fractals 34 (2007), 213-223.
DOI
|
13 |
H. Haase, A contribution to measure and dimension of metric spaces, Math. Nachr. 124 (1985), 45-55.
DOI
|
14 |
M. Das, Billingsley's packing dimension, Proceedings of the American Mathematical Society 136 (2008), 273-278.
DOI
|
15 |
M. Das, Hausdorff measures, dimensions and mutual singularity, Transactions of the American Mathematical Society 357 (2005), 4249-4268.
DOI
|
16 |
Z. Douzi and B. Selmi, Multifractal variation for projections of measures, Chaos, Solitons and Fractals 91 (2016), 414-420.
DOI
|
17 |
G. A. Edgar, Integral, probability, and fractal measures, Springer-Verlag, New York, (1998).
|
18 |
K. J. Falconer, Fractal geometry: mathematical foundations and applications, Chichester (1990). Wiley.
|
19 |
H. Haase, Open-invariant measures and the covering number of sets, Math. Nachr. 134 (1987), 295-307.
DOI
|
20 |
E. 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).
|
21 |
S. Jurina, N. MacGregor, A. Mitchell, L. Olsen and A. Stylianou, On the Hausdorff and packing measures of typical compact metric spaces, Aequationes Mathematicae 92 (2018), 709-735.
DOI
|
22 |
M. Khelifi, H. Lotfi, A. Samti and B. Selmi, A relative multifractal analysis, Chaos, Solitons and Fractals, (to appear).
|
23 |
M. Dai, X. Peng and W. Li, Relative multifractal analysis in a probability space, Interna Journal of Nonlinear Science 10 (2010), 313-319.
|
24 |
Q. Liu, Local dimensions of the measure on a Galtion-Watson tree, Ann. Inst. H. Poincare, Probabilites et Statistiques 37 (2001), 195-222.
DOI
|
25 |
L. Olsen, On average Hewitt-Stromberg measures of typical compact metric spaces, Mathematische Zeitschrift 293 (2019), 1201-1225.
DOI
|
26 |
Q. Liu, Exact packing measure on a Galton-Watson tree, Stochastic Processes and their Applications 85 (2000), 19-28.
DOI
|
27 |
P. Mattila, Geometry of sets and measures in euclidian spaces: Fractals and Rectifiability, Cambridge University Press (1995).
|
28 |
A. Mitchell and L. Olsen, Coincidence and noncoincidence of dimensions in compact subsets of [0, 1], arXiv:1812.09542v1, (2018).
|
29 |
C. Qing-Jiang and Q. Xiao-Gang, Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases, Chaos, Solitons and Fractals 41 (2009), 1676-1683.
DOI
|
30 |
Y. Pesin, Dimension theory in dynamical systems, Contemporary views and applications, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, (1997).
|
31 |
J. M. Rey, The role of Billingsley dimensions in computing fractal dimensions on Cantor-like spaces, Proceedings of the American Mathematical Society 128 (1999), 561-572.
DOI
|
32 |
B. Selmi, On the strong regularity with the multifractal measures in a probability space, Anal. Math. Phys. 9 (2019), 1525-1534
DOI
|
33 |
B. Selmi, On the effect of projections on the Billingsley dimensions. Asian-European Journal of Mathematics 13 (2020), 2050128/1-17.
DOI
|
34 |
B. Selmi, On the projections of the multifractal Hewitt-Stromberg dimension functions, arXiv:1911.09643v1
|
35 |
O. Zindulka, Packing measures and dimensions on Cartesian products, Publ. Mat. 57 (2013), 393-420.
DOI
|