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Showing 1 to 4 of 4 for “"Exceptional set"”.
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Higher-Dimensional Analogues of Two Theorems of Orponen on Exceptional Sets
Let $A \subseteq \mathbb{R}^n$ 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 …
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Rationing in Emergency Ireland, 1939-48
… measures; the Irish government assumed an exceptional set of dictatorial-like powers under the Emergency Powers Act (EPA), 1939. This act formed the basis for government control which extended to all facets of life in Emergency Ireland including censorship, internment, travel restrictions, …
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Absolutely Continuous Stationary Measures
… of stationary measures. Given a finite set of measurable maps $S_1, S_2, \dots, S_n$ on a measurable set $X$ and a probability vector $p_1, p_2, \dots, p_n$ we say that a probability measure $\nu$ on $X$ is stationary if $\begin{equation*} \nu = \sum_{i=1}^{n} p_i \nu \circ S_i^{-1}. …
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On the Variational Theory of Yang-Mills-Higgs Energies and the Structure of the Singular Set of $\mathbb{Z}$$_{2}$-Harmonic Spinors
… theory introduced by Almgren and Pitts in the setting of geometric measure theory. In particular, we prove that min-max values for the latter always provide a lower bound for the former. En route to proving this comparison, we introduce the gradient flow of the Yang-Mills-Higgs energies and …