Integral Menger curvature and rectifiability of $n$-dimensional Borel sets in Euclidean $N$-space
نویسندگان
چکیده
منابع مشابه
Menger curvature and rectifiability
E3 c(x, y, z)dH(x)dH(y)dH(z) where H1 is the 1-dimensional Hausdorff measure in Rn, c(x, y, z) is the inverse of the radius of the circumcircle of the triangle (x, y, z), that is, following the terminology of [6], the Menger curvature of the triple (x, y, z). A Borel set E ⊂ Rn is said to be “purely unrectifiable” if for any Lipschitz function γ : R → Rn, H1(E ∩ γ(R)) = 0 whereas it is said to ...
متن کاملMenger Curvature and Rectifiability 833
where H1 is the 1-dimensional Hausdorff measure in Rn, c(x, y, z) is the inverse of the radius of the circumcircle of the triangle (x, y, z), that is, following the terminology of [6], the Menger curvature of the triple (x, y, z). A Borel set E ⊂ Rn is said to be “purely unrectifiable” if for any Lipschitz function γ : R → Rn, H1(E ∩ γ(R)) = 0 whereas it is said to be rectifiable if there exist...
متن کاملBEST APPROXIMATION SETS IN -n-NORMED SPACE CORRESPONDING TO INTUITIONISTIC FUZZY n-NORMED LINEAR SPACE
The aim of this paper is to present the new and interesting notionof ascending family of $alpha $−n-norms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an $alpha $−n-normedspace corresponding to an intuitionistic fuzzy n-normed linear space is alsodefined and several related results are obtained.
متن کاملPath integral treatment of a family of super-integrable systems in n-dimensional Euclidean space
The exact path integration for a family of maximally super-integrable systems generalizing the hydrogen atom in the n-dimensional Euclidean space is presented. The Green’s function is calculated in parabolic rotational and spherical coordinate systems. The energy spectrum and the correctly normalized wave functions of the bound states are obtained from the poles of the Green’s function and thei...
متن کاملOn the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space
The theory of the isoptic curves is widely studied in the Euclidean plane E2 (see [1] and [13] and the references given there). The analogous question was investigated by the authors in the hyperbolic H2 and elliptic E2 planes (see [3], [4]), but in the higher dimensional spaces there is no result according to this topic. In this paper we give a natural extension of the notion of the isoptic cu...
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: 2017
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7011