Hausdorff measures, dimensions and mutual singularity
نویسندگان
چکیده
منابع مشابه
Spectral Measures with Arbitrary Hausdorff Dimensions
In this paper, we consider spectral properties of Riesz product measures supported on homogeneous Cantor sets and we show the existence of spectral measures with arbitrary Hausdorff dimensions, including non-atomic zero-dimensional spectral measures and one-dimensional singular spectral measures.
متن کاملHausdorff measures and dimensions in non equiregular sub-Riemannian manifolds
This paper is a starting point towards computing the Hausdorff dimension of submanifolds and the Hausdorff volume of small balls in a sub-Riemannian manifold with singular points. We first consider the case of a strongly equiregular submanifold, i.e., a smooth submanifold N for which the growth vector of the distribution D and the growth vector of the intersection of D with TN are constant on N...
متن کاملHausdorff measures of different dimensions are not Borel isomorphic
We show that Hausdorff measures of different dimensions are not Borel isomorphic; that is, the measure spaces (R, B, H) and (R, B, H) are not isomorphic if s 6= t, s, t ∈ [0, 1], where B is the σ-algebra of Borel subsets of R and H is the d-dimensional Hausdorff measure. This answers a question of B. Weiss and D. Preiss. To prove our result, we apply a random construction and show that for ever...
متن کاملOn Hausdorff Distance Measures
A number of Hausdorff-based algorithms have been proposed for finding objects in images. We evaluate different measures and argue that the Hausdorff Average distance measure outperforms other variants for model detection. This method has improved robustness properties with respect to noise. We discuss the algorithms with respect to typical classes of noise, and we illustrate their relative perf...
متن کاملHausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations
We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation. We give a formula of the dimensions of such measur...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-04031-6