The $(\varphi , 1)$ rectifiable subsets of Euclidean space
نویسندگان
چکیده
منابع مشابه
Subsets of Rectifiable curves in Hilbert Space-The Analyst’s TSP
We study one dimensional sets (Hausdorff dimension) lying in a Hilbert space. The aim is to classify subsets of Hilbert spaces that are contained in a connected set of finite Hausdorff length. We do so by extending and improving results of Peter Jones and Kate Okikiolu for sets in Rd . Their results formed the basis of quantitative rectifiability in Rd . We prove a quantitative version of the f...
متن کاملComputability on Regular Subsets of Euclidean Space
For the computability of subsets of real numbers, several reasonable notions have been suggested in the literature. We compare these notions in a systematic way by relating them to pairs of ‘basic’ ones. They turn out to coincide for full-dimensional convex sets; but on the more general class of regular sets, they reveal rather interesting ’weaker/stronger’ relations. This is in contrast to sin...
متن کاملOn the Asymptotic Magnitude of Subsets of Euclidean Space
‘Magnitude’ is a canonical invariant of finite metric spaces which has its origins in category theory; it is analogous to cardinality of finite sets. Here, by approximating certain compact subsets of Euclidean space with finite subsets, the magnitudes of line segments, circles and Cantor sets are defined and calculated. It is observed that asymptotically these satisfy the inclusion-exclusion pr...
متن کاملOn radii of spheres determined by subsets of Euclidean space
In this paper we consider the problem that how large the Hausdorff dimension of E ⊂ Rd needs to be to ensure the radii set of (d − 1)-dimensional spheres determined by E has positive Lebesgue measure. We obtain two results. First, by extending a general mechanism for studying Falconer-type problems in [4], we prove that it holds when dimH(E) > d− 1+ 1 d and in R2, the index 3 2 is sharp for thi...
متن کاملCharacterizations of Slant Ruled Surfaces in the Euclidean 3-space
In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...
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: 1978
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1978-0487725-x