On linear sets of points of fractional dimension

  title={On linear sets of points of fractional dimension},
  author={A. Besicovitch},
  journal={Mathematische Annalen},
Dynamics of the scenery flow and conical density theorems
Conical density theorems are used in the geometric measure theory to derive geometric information from given metric information. The idea is to examine how a measure is distributed in small balls.Expand
Dynamics of the scenery flow and geometry of measures
We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conicalExpand
Scenery flow, conical densities, and rectifiability
We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review theExpand
Ergodic Theory on Homogeneous Spaces and Metric Number Theory
  • D. Kleinbock
  • Mathematics, Computer Science
  • Encyclopedia of Complexity and Systems Science
  • 2009
An overview of recent developments in metric number theory, in particular, Diophantine approximation on manifolds, obtained by applying ideas and methods coming from dynamics on homogeneous spaces is given. Expand
Comparing Packing Measures to Hausdorff Measures on the Line
For each 0 < s < 1, define c(s) = inf E Ps(E) Hs(E) , where Ps, Hs denote respectively the s–dimensional packing measure and Hausdorff measure, and the infimum is taken over all the sets E ⊂ R with 0Expand
Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization
Although concrete operators with singular continuous spectrum have proliferated recently [7,11,13,17,34,35,37,39], we still don’t really understand much about singular continuous spectrum. In part,Expand
Hidden chaos factors inducing random walks as a factor restricting hospital operative efficiency
La Fuenfria Hospital (LFH) operative parameters such as: hospitalised patients; daily admissions and discharges were studies for the hospital as a whole, and per each Hospital's service unit (justExpand