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Hausdorff dimension and capacities of intersections of sets inn-space

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References

  • [A]Almgren Jr., F. J., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints.Mem. Amer. Math. Soc., no. 165, 1976.

  • [BM]Besicovitch, A. S. &Moran, P. A. P., The measure of product and cylinder sets.J. London Math. Soc., 20 (1945), 110–120.

    MATH  MathSciNet  Google Scholar 

  • [D]Dellacherie, C.,Ensembles analytiques, capacités, mesures de Hausdorff. Springer-Verlag, Berlin and New York, 1972.

    MATH  Google Scholar 

  • [F]Federer, H.,Geometric measure theory. Springer-Verlag, Berlin and New York, 1969.

    MATH  Google Scholar 

  • [H1]Hawkes, J., Hausdorff measure, entropy, and the independence of small sets.Proc. London Math. Soc. (3), 28 (1974), 700–724.

    MATH  MathSciNet  Google Scholar 

  • [H2]—, Some algebraic properties of small sets.Quart. J. Math. Oxford (3), 26 (1975), 195–201.

    MATH  MathSciNet  Google Scholar 

  • [H]Hutchinson, J. E., Fractals and self similarity.Indiana Univ. Math. J., 30 (1981), 713–747.

    Article  MATH  MathSciNet  Google Scholar 

  • [L]Landkof, N. S.,Foundations of modern, potential theory. Springer-Verlag, Berlin and New York, 1972.

    MATH  Google Scholar 

  • [LV]Luukkainen, J. &Väisälä, J., Elements of Lipschitz topology.Ann. Acad. Sci. Fenn. Ser. A I, 3 (1977), 85–122.

    MATH  Google Scholar 

  • [MB]Mandelbrot, B.,Fractals;, from, chance, and dimension. Freeman San Francisco, 1977.

    Google Scholar 

  • [MJ]Marstrand, J. M., Some fundamental geometrical properties of plane sets of fractional dimensions.Proc. London Math. Soc. (3), 4 (1954), 257–302.

    MATH  MathSciNet  Google Scholar 

  • [MP1]Mattila, P., Hausdorff dimension, orthogonal projections and intersections with planes.Ann. Acad. Sci. Fenn. Ser. A I, 1 (1975), 227–244.

    MATH  MathSciNet  Google Scholar 

  • [MP2]—, Integralgeometric properties of capacities.Trans. Amer. Math. Soc., 266 (1981), 539–554.

    Article  MATH  MathSciNet  Google Scholar 

  • [MP3]Mattila, P., An integral inequality for capacities.Math. Scand., 53 (1983).

  • [T]Tricot Jr., C., Two definitions of fractional dimension.Math. Proc. Camb. Phil. Soc., 91 (1982), 57–74.

    Article  MATH  MathSciNet  Google Scholar 

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Mattila, P. Hausdorff dimension and capacities of intersections of sets inn-space. Acta Math 152, 77–105 (1984). https://doi.org/10.1007/BF02392192

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