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A zero-one half law for porosity of measures

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2000
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Facultad de Ciencias Económicas y Empresariales. Decanato
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Abstract
We prove that the upper porosity of any Radon probability measure is either 0 or 1/2
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Probabilidades (Matemáticas)
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Coifmann, R.R. and G. Weiss, Analyse Harmonique Non-commutative sur Certains Espaces Homogènes, Lectures Notes in Math. vol. 242 (1971), Springer-Verlag. Federer, H., Geometric Measure Theory (1969), Springer Verlag. Eckmann, J.P., E. Järvenpää and M. Järvenpää, Porosities and Dimensions of Measures, Nonlinearity 13 (2000), 1-18. Guzmán, M. de, Differentiation of Integrals in IRn, Lectures Notes in Math. Vol. 481 (1975), Springer-Verlag. Mattila, P., Geometry of sets and measures in Euclidean spaces (1995), Cambridge University Press. Preiss, D., Geometry of mensures in IRn, Ann. of Math.,(2) 125 (1987), 537-643. Salli, A., On the Minkowski dimension of strongly porous fractal sets in IRn, Proc. London Math. Soc, (3) 62 (1991), 353-372. Thomson, B.S., Real Functions, Lectures Notes in Math, vol. 1170 (1985), Springer-Verlag. Zajicek, L., Porosity and o-porosity, Real Analysis Exchange, 13 (1987-88), 314-350.
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https://hdl.handle.net/20.500.14352/64137
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