Geodesic
A new proof of Federer’s structure theorem for 𝑘-dimensional subsets of 𝐑^{𝐍}
White, Brian 1
1 Department of Mathematics, Stanford University, Stanford, California 94305
Journal of the American Mathematical Society, Tome 11 (1998) no. 3, pp. 693-701 Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

We prove that Federer’s structure theorem for $k$-dimensional sets in $\mathbf {R}^{N}$ follows from the special case of $1$-dimensional sets in the plane, which was proved earlier by Besicovitch.
DOI : 10.1090/S0894-0347-98-00267-7

White, Brian  1

1 Department of Mathematics, Stanford University, Stanford, California 94305 
@article{10_1090_S0894_0347_98_00267_7,
     author = {White, Brian},
     title = {A new proof of {Federer{\textquoteright}s} structure theorem for \ensuremath{\mathit{k}}-dimensional subsets of {\ensuremath{\mathbf{R}}^{\ensuremath{\mathbf{N}}}}},
     journal = {Journal of the American Mathematical Society},
     pages = {693--701},
     year = {1998},
     volume = {11},
     number = {3},
     doi = {10.1090/S0894-0347-98-00267-7},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-98-00267-7/}
}
TY  - JOUR
AU  - White, Brian
TI  - A new proof of Federer’s structure theorem for 𝑘-dimensional subsets of 𝐑^{𝐍}
JO  - Journal of the American Mathematical Society
PY  - 1998
SP  - 693
EP  - 701
VL  - 11
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-98-00267-7/
DO  - 10.1090/S0894-0347-98-00267-7
ID  - 10_1090_S0894_0347_98_00267_7
ER  - 
%0 Journal Article
%A White, Brian
%T A new proof of Federer’s structure theorem for 𝑘-dimensional subsets of 𝐑^{𝐍}
%J Journal of the American Mathematical Society
%D 1998
%P 693-701
%V 11
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-98-00267-7/
%R 10.1090/S0894-0347-98-00267-7
%F 10_1090_S0894_0347_98_00267_7
White, Brian. A new proof of Federer’s structure theorem for 𝑘-dimensional subsets of 𝐑^{𝐍}. Journal of the American Mathematical Society, Tome 11 (1998) no. 3, pp. 693-701. doi: 10.1090/S0894-0347-98-00267-7

[1] Falconer, K. J. The geometry of fractal sets 1986

[2] Birkhoff, Garrett, Ward, Morgan A characterization of Boolean algebras Ann. of Math. (2) 1939 609 610

[3] Federer, Herbert Geometric measure theory 1969

[4] Mattila, Pertti Geometry of sets and measures in Euclidean spaces 1995

[5] Simon, Leon Lectures on geometric measure theory 1983

Cité par Sources :