Geodesic
A SHORT NOTE ON ENHANCED DENSITY SETS
Glasgow mathematical journal, Tome 53 (2011) no. 3, pp. 631-635

Voir la notice de l'article provenant de la source Cambridge

DOI

We give a simple proof of a statement extending Fu's (J.H.G. Fu, Erratum to ‘some remarks on legendrian rectiable currents’, Manuscripta Math. 113(3) (2004), 397–401) result: ‘If Ω is a set of locally finite perimeter in R2, then there is no function f ∈ C1(R2) such that ∇f(x1, x2) = (x2, 0) at a.e. (x1, x2) ∈ Ω’. We also prove that every measurable set can be approximated arbitrarily closely in L1 by subsets that do not contain enhanced density points. Finally, we provide a new proof of a Poincaré-type lemma for locally finite perimeter sets, which was first stated by Delladio (S. Delladio, Functions of class C1 subject to a Legendre condition in an enhanced density set, to appear in Rev. Mat. Iberoamericana).
DOI : 10.1017/S001708951100022X
Mots-clés : Primary 28Axx, 28A75, 49Q15, Secondary 26A45 
DELLADIO, SILVANO. A SHORT NOTE ON ENHANCED DENSITY SETS. Glasgow mathematical journal, Tome 53 (2011) no. 3, pp. 631-635. doi: 10.1017/S001708951100022X
@article{10_1017_S001708951100022X,
     author = {DELLADIO, SILVANO},
     title = {A {SHORT} {NOTE} {ON} {ENHANCED} {DENSITY} {SETS}},
     journal = {Glasgow mathematical journal},
     pages = {631--635},
     year = {2011},
     volume = {53},
     number = {3},
     doi = {10.1017/S001708951100022X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951100022X/}
}
TY  - JOUR
AU  - DELLADIO, SILVANO
TI  - A SHORT NOTE ON ENHANCED DENSITY SETS
JO  - Glasgow mathematical journal
PY  - 2011
SP  - 631
EP  - 635
VL  - 53
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708951100022X/
DO  - 10.1017/S001708951100022X
ID  - 10_1017_S001708951100022X
ER  - 
%0 Journal Article
%A DELLADIO, SILVANO
%T A SHORT NOTE ON ENHANCED DENSITY SETS
%J Glasgow mathematical journal
%D 2011
%P 631-635
%V 53
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708951100022X/
%R 10.1017/S001708951100022X
%F 10_1017_S001708951100022X

Cité par Sources :