نتایج جستجو برای: hausdorff measure of noncompactness

تعداد نتایج: 21174748  

2009
Shin-ichi OHTA

We give a necessary and sufficient condition on a Randers space for the existence of a measure for which Shen’s S-curvature vanishes everywhere. Moreover, such a measure coincides with the Busemann-Hausdorff measure up to a constant multiplication.

2010
Leon Simon

In this article we describe recent (within the past 4 or 5 years) results in minimal surface theory, with particular emphasis on the existence and regularity theory. For a more general survey, including some technical background discussion and a more comprehensive bibliography, the reader is referred to [30]. Throughout the article «?f will denote ÄJ-dimensional Hausdorff measure (in Euclidean ...

2015
JONAS AZZAM

In the present paper we sketch the proof of the fact that for any open connected set Ω ⊂ Rn+1, n ≥ 1, and any E ⊂ ∂Ω with 0 < H(E) < ∞, absolute continuity of the harmonic measure ω with respect to the Hausdorff measure on E implies that ω|E is rectifiable.

1998
BRIAN WHITE

If X is a subset of R , let Hk(X) denote the k-dimensional hausdorff measure of X . We write Ik(X) = 0 if H(πKX) = 0 for almost every k-plane K in R , where πK : R → K is orthogonal projection. Otherwise we write Ik(X) > 0. This paper gives a proof of the following theorem. 1.1. Structure Theorem. Let X be a set in R with Hk(X) < ∞ and Ik(X) > 0. Then there is a k-dimensional C submanifold M wi...

1998
Dong-Gyu Sim Rae-Hong Park

This paper proposes an oriented Hausdorff similarity measure for object matching. The oriented Hausdorff distance (HD) measure is introduced by replacing the distance concept of conventional HD algorithms by a similarity measure. The orientation at each ~ i x e l is used for removing incorrect correspondences. Various experiments show that the perFigure 1: Block diagram for the Hausdorff distan...

2015
Serena Doria

Let (Ω, d) be a metric space where Ω is a set with positive and finite Hausdorff outer measure in its Hausdorff dimension and let B be a partition of Ω. The coherent upper conditional prevision defined as the Choquet integral with respect to its associated Hausdorff outer measure is proven to satisfy the disintegration property and the conglomerative principle on every partition.

2007
G. A. Edgar

We have collected definitions and basic results for the (centered ball) density in metric space with respect to an arbitrary Hausdorff function. We have kept the definitions general: we do not assume the Hausdorff functions are continuous or blanketed, and we do not assume the metric space is a subset of Euclidean space. We discuss the covering measure (= centered Hausdorff measure) and packing...

2005
Bogdan Bojarski Paweł Strzelecki

We prove various generalizations of classical Sard’s theorem to mappings f : M → N between manifolds in Hölder and Sobolev classes. It turns out that if f ∈ C(M,N), then—for arbitrary k and λ—one can obtain estimates of the Hausdorff measure of the set of critical points in a typical level set f−1(y). The classical theorem of Sard holds true for f ∈ C with sufficiently large k, i.e., k > max(m−...

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