Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions
From MaRDI portal
Publication:5828125
DOI10.1112/plms/s3-4.1.257zbMath0056.05504OpenAlexW2120045167MaRDI QIDQ5828125
Publication date: 1954
Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1112/plms/s3-4.1.257
Related Items
On Hausdorff dimension of projections, On the Origins, Nature, and Impact of Bourgain’s Discretized Sum-Product Theorem, Projections and slices of measures, Geometry of planar curves intersecting many lines at a few points, Hausdorff Dimension Exceptional Set Estimates for Projections, Sections and Intersections, An exceptional set for Hausdorff dimension, Gaussian sample functions and the Hausdorff dimension of level crossings, Dimensions of slices through the Sierpiński gasket, Dynamics of the scenery flow and conical density theorems, Fractal percolations, On the projections of mutual L^{q,t}-spectrum, Projections of mutual multifractal functions, On dimensions of visible parts of self-similar sets with finite rotation groups, Order‐two density of sets and measures with non‐integral dimension, A note on the relative growth of products of multiple partial quotients in the plane, Transversal families of nonlinear projections and generalizations of Favard length, Restricted families of projections onto planes: the general case of nonvanishing geodesic curvature, Dimensions of projected sets and measures on typical self-affine sets, Vertical projections in the Heisenberg group via cinematic functions and point-plate incidences, Projection theorems for linear-fractional families of projections, An exceptional set estimate for restricted projections to lines in \(\mathbb{R}^3\), Examples of \(d\)-sets with irregular projection of Hausdorff measures, On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane, Projection estimates for the lower Hewitt-Stromberg dimension, Conditions for subharmonicity and subharmonic extensions of functions, Projection theorems using effective dimension, A nonlinear projection theorem for Assouad dimension and applications, On the Ledrappier–Young formula for self-affine measures, On the dimension of visible parts, Attainable values for the Assouad dimensionof projections, Unnamed Item, A generalization of O’Neil’s theorems for projections of measures and dimensions, Kaufman and Falconer estimates for radial projections and a continuum version of Beck's theorem, Length of sets under restricted families of projections onto lines, A sharp exceptional set estimate for visibility, Marstrand-type Theorems for the Counting and Mass Dimensions in ℤ, An a.e. lower bound for Hausdorff dimension under vertical projections in the Heisenberg group, Self-Similar Sets: Projections, Sections and Percolation, Random Covering Sets, Hitting Probabilities and Variants of the Covering Problem, Projections in vector spaces over finite fields, The packing dimension of projections and sections of measures, Intersecting self-similar Cantor sets, Projections of Gibbs measures on self-conformal sets, Projection theorems for box and packing dimensions, A probabilistic Takens theorem, Fractal Intersections and Products via Algorithmic Dimension, Geometric bounds for Favard length, ON THE DIMENSION OF SELF-SIMILAR SETS, A large plane set intersecting lines in infinitely many directions in at most one point, Planar self-affine sets with equal Hausdorff, box and affinity dimensions, Linear response theory for diffeomorphisms with tangencies of stable and unstable manifolds—a contribution to the Gallavotti–Cohen chaotic hypothesis, Spatially independent martingales, intersections, and applications, Combinatorial proofs of two theorems of Lutz and Stull, The visible part of plane self-similar sets, Dimension of slices through the Sierpinski carpet, From Apollonius to Zaremba: Local-global phenomena in thin orbits, ON INTERSECTING IFS FRACTALS WITH LINES, Projections of Measures Invariant Under the Geodesic Flow, Unnamed Item, Estimators of fractal dimension: assessing the roughness of time series and spatial data, Interval projections of self-similar sets, Visible part of dominated self-affine sets in the plane, Prevalence, QUATERNION DYNAMICS AND FRACTALS IN ℝ4, Exact dimensionality and projection properties of Gaussian multiplicative chaos measures, On the effect of projections on the Billingsley dimensions, Unnamed Item, Ergodicity of unipotent flows and Kleinian groups, Projections of fractal percolations, Dynamics of the scenery flow and geometry of measures, Intermediate Dimensions: A Survey, Fractal Geometry of Bedford-McMullen Carpets, Some Variants of Orponen’s Theorem on Visible Parts of Fractal Sets, Relative multifractal box-dimensions, The Geometry of Fractal Percolation, On the Projections of the Mutual Multifractal Renyi Dimensions, Algorithmic Fractal Dimensions in Geometric Measure Theory, Slices of Hewitt-Stromberg measures and co-dimensions formula, Homoclinic tangencies for hyperbolic sets of large Hausdorff dimension, Assouad dimension influences the box and packing dimensions of orthogonal projections, Dimension distortion by right coset projections in the Heisenberg group, Hausdorff dimension of intersections with planes and general sets, On arithmetic sums of Ahlfors-regular sets, Projections of planar sets in well-separated directions, Projections of measures with small supports, Digital sundials, paradoxical sets, and Vitushkin's conjecture, Superbranching processes and projections of random Cantor sets, Projections of self-similar sets with no separation condition, Lower bounds for dimensions of sums of sets, Projecting the one-dimensional Sierpiński gasket, Projection theorems for Hewitt-Stromberg and modified intermediate dimensions, On restricted families of projections in ℝ3, Exact dimensionality and projections of random self-similar measures and sets, Generating hierarchial scale-free graphs from fractals, Distance sets, orthogonal projections and passing to weak tangents, Dimension formula for random transformations, Integrability of orthogonal projections, and applications to Furstenberg sets, An exact formula for the measure dimensions associated with a class of piecewise linear maps, How large dimension guarantees a given angle?, Local dimensions of sliced measures and stability of packing dimensions of sections of sets, Intersection-equivalence of Brownian paths and certain branching processes, On the projections of generalized upper \(L^q\)-spectrum, Multifractal variation for projections of measures, Lower bounds for the Hausdorff dimension of \(n\)-dimensional self-affine sets, Fractal properties of products and projections of measures in ℝd, Geometry of measures in real dimensions via Hölder parameterizations, Generic Hölder level sets and fractal conductivity, Yet another proof of Marstrand's theorem, Potential method and projection theorems for macroscopic Hausdorff dimension, The Hausdorff dimension of some fractals and attractors of overlapping construction, The effect of projections on dimension in the Heisenberg group, On the dimension and smoothness of radial projections, Projection and slicing theorems in Heisenberg groups, Intersection of Mcmullen set with its rational translation, Reflectionless measures for Calderón-Zygmund operators. II: Wolff potentials and rectifiability, Slicing sets and measures, and the dimension of exceptional parameters, Hausdorff dimension and non-degenerate families of projections, Marstrand's theorem revisited: projecting sets of dimension zero, Intersecting random translates of invariant Cantor sets, Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets, Projection theorems in hyperbolic space, Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions, Working session: Additive combinatorics, entropy, and fractal geometry. Abstracts from the working session held October 8--13, 2017, Who Asked Us? How the Theory of Computing Answers Questions about Analysis, A Marstrand theorem for measures with polytope density, On the Hausdorff dimension of fibres, A generalization of Marstrand's theorem for projections of Cartesian products, When Cantor Sets Intersect Thickly, On the distance sets of Ahlfors-David regular sets, New dimension spectra: finer information on scaling and homogeneity, Intersections of projections and slicing theorems for the isotropic Grassmannian and the Heisenberg group, Multifractal analysis for projections of Gibbs and related measures, Conical upper density theorems and porosity of measures, Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes, Dimension of slices through fractals with initial cubic pattern, A note on the density of 𝑠-dimensional sets, Wavelet transforms and order-two densities of fractals, Inconstancy of finite and infinite sequences, A combinatorial proof of Marstrand's theorem for products of regular Cantor sets, Sequences that omit a box (modulo 1), Hausdorff dimension estimates for restricted families of projections in \(\mathbb{R}^3\), (Non)regularity of projections of measures invariant under geodesic flow, Metric characterization of pure unrectifiability, Sections of Sets of zero Lebesgue measure, On the Relations Between 2D and 3D Fractal Dimensions: Theoretical Approach and Clinical Application in Bone Imaging, Tangential behavior of functions and conical densities of Hausdorff measures, Are lines much bigger than line segments?, Quantitative visibility estimates for unrectifiable sets in the plane, Lebesgue density influences Hausdorff measure; large sets surface‐like from many directions, A capacity approach to box and packing dimensions of projections of sets and exceptional directions, Projection theorems for intermediate dimensions, Geodesic interpolation on Sierpiński gaskets, Marstrand type projection theorems for normed spaces, Upper porous measures on metric spaces, Dimensions of projections of sets on Riemannian surfaces of constant curvature, Multifractal geometry of slices of measures, On Hausdorff dimension of radial projections, Sixty Years of Fractal Projections, Scenery Flow, Conical Densities, and Rectifiability, Projections of Self-Similar and Related Fractals: A Survey of Recent Developments, Hausdorff dimension, intersections of projections and exceptional plane sections, A note on the 1-prevalence of continuous images with full Hausdorff dimension, An improved bound on the packing dimension of Furstenberg sets in the plane, Projections of random Cantor sets, Convex bodies with almost all k-dimensional sections polytopes, A proof of Furstenberg's conjecture on the intersections of \(\times p\)- and \(\times q\)-invariant sets, Hausdorff dimension and projections related to intersections, The multifractal spectra of projected measures in Euclidean spaces, Hausdorff and packing dimensions and sections of measures, Local conical dimensions for measures, On the projections of the multifractal packing dimension for \(q > 1\), Self-similar measures and intersections of Cantor sets, Hausdorff dimension and the exceptional set of projections, Hausdorff dimension and capacities of intersections of sets in n-space, Improved bounds for restricted projection families via weighted Fourier restriction, Geometric properties of images of cartesian products of regular Cantor sets by differentiable real maps, On the packing dimension and category of exceptional sets of orthogonal projections
