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 University Press

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
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