Свойство выпуклости взаимных мультифрактальных размерностей
Problemy analiza, no. 17 (2010), pp. 15-24.

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It has received that the mutual packing dimension of subset $E$ of set $\mathrm{supp}~\mu\cap\mathrm{supp}~\nu$ for Borel probability measures $\mu$ and $\nu$ is convex, but the mutual Hausdorff dimension of $E$ satisfies the condition of weak convexity.
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     author = {N. Yu. Svetova},
     title = {{\CYRS}{\cyrv}{\cyro}{\cyrishrt}{\cyrs}{\cyrt}{\cyrv}{\cyro} {\cyrv}{\cyrery}{\cyrp}{\cyru}{\cyrk}{\cyrl}{\cyro}{\cyrs}{\cyrt}{\cyri} {\cyrv}{\cyrz}{\cyra}{\cyri}{\cyrm}{\cyrn}{\cyrery}{\cyrh} {\cyrm}{\cyru}{\cyrl}{\cyrsftsn}{\cyrt}{\cyri}{\cyrf}{\cyrr}{\cyra}{\cyrk}{\cyrt}{\cyra}{\cyrl}{\cyrsftsn}{\cyrn}{\cyrery}{\cyrh} {\cyrr}{\cyra}{\cyrz}{\cyrm}{\cyre}{\cyrr}{\cyrn}{\cyro}{\cyrs}{\cyrt}{\cyre}{\cyrishrt}},
     journal = {Problemy analiza},
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N. Yu. Svetova. Свойство выпуклости взаимных мультифрактальных размерностей. Problemy analiza, no. 17 (2010), pp. 15-24. http://geodesic.mathdoc.fr/item/PA_2010_17_a1/

[1] Pesin Ya. B., Teoriya razmernostei i dinamicheskie sistemy: sovremennyi vzglyad i prilozheniya, Izd-vo instituta kompyuternykh issledovanii, M.; Izhevsk, 2002, 404 pp.

[2] Bogachev V. I., Osnovy teorii mery, v 2 t., v. 1, Izd-vo NITs Regulyarnaya i khaoticheskaya dinamika, M.; Izhevsk, 2003, 544 pp.

[3] Rokafellar R., Vypuklyi analiz, Mir, M., 1973, 471 pp.

[4] Svetova N. Yu., “Vzaimnye multifraktalnye spektry I. Tochnye spektry”, Trudy PetrGU. Ser. Matematika, 2004, no. 11, 42–47 | MR

[5] Federer G., Geometricheskaya teoriya mery, Nauka, M., 1987, 760 pp. | MR | Zbl

[6] Falconer K. J., Fractal geometry. Mathematical Foundations and Applications, John Wiley Sons, New York, 1990, 337 pp. | MR | Zbl

[7] Olsen L., “A multifractal formalism”, Advances in mathematics, 1995, no. 116, 82–195 | DOI | MR

[8] Olsen L., “Multifractal geometry”, Progress in probability, 46 (2000), 3–37 | MR | Zbl