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Showing 1 to 3 of 3 for “"packing dimension"”.
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Higher-Dimensional Analogues of Two Theorems of Orponen on Exceptional Sets
… \mathbb{R}^n$ be a Borel set of Hausdorff dimension $\dim_{\mathrm H} A = s$ and, for each $m$-plane $V$ in the Grassmannian $\mathbf{Gr}(n,m)$, let $\pi_V : \mathbb{R}^n \to V$ be the orthogonal projection of $\mathbb{R}^n$ onto $V$. \textit{Marstrand's projection theorem} states that …
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Computability and Fractal Dimension
… theory and various notions of fractal dimension, mainly Hausdorff dimension. An algorithmic approach to Hausdorff measures makes it possible to define the Hausdorff dimension of individual points instead of sets in a metric space. This idea was first realized by Lutz (2000). Working in …
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Dimensions in Random Constructions.
… prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.