0000000000274245
AUTHOR
Kenneth J. Falconer
The packing dimension of projections and sections of measures
AbstractWe show that for a probability measure μ on ℝnfor almost all m–dimensional subspaces V, provided dimH μ≤m. Here projv denotes orthogonal projection onto V, and dimH and dimp denote the Hausdorff and packing dimension of a measure. In the case dimH μ > m we show that at μ-almost all points x the slices of μ by almost all (n − m)-planes Vx through x satisfyWe give examples to show that these inequalities are sharp.
Packing dimensions of sections of sets
We obtain a formula for the essential supremum of the packing dimensions of the sections of sets parallel to a given subspace. This depends on a variant of packing dimension defined in terms of local projections of sets.