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Hausdorff and packing dimensions and sections of measures
Published online by Cambridge University Press: 26 February 2010
Abstract
Let m and n be integers with 0<m<n and let μ be a Radon measure on ℝn with compact support. For the Hausdorff dimension, dimH, of sections of measures we have the following equality: for almost all (n − m)-dimensional linear subspaces V
provided that dimH μ > m. Here μv,a is the sliced measure and V⊥ is the orthogonal complement of V. If the (m + d)-energy of the measure μ is finite for some d>0, then for almost all (n − m)-dimensional linear subspaces V we have
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- Copyright © University College London 1998
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