Search results
Search: MSC category 28A75
( Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] )
1. CMB 2010 (vol 54 pp. 172)
 Shayya, Bassam

Measures with Fourier Transforms in $L^2$ of a Halfspace
We prove that if the Fourier transform of a compactly supported
measure is in $L^2$ of a halfspace, then the measure is
absolutely continuous to Lebesgue measure. We then show how this
result can be used to translate information about the
dimensionality of a measure and the decay of its Fourier
transform into geometric information about its support.
Categories:42B10, 28A75 

2. CMB 1997 (vol 40 pp. 3)
 Ayari, S.; Dubuc, S.

La formule de Cauchy sur la longueur d'une courbe
Pour toute courbe rectifiable du plan, nous d\'emontrons la formule
de Cauchy relative \`a sa longueur. La formule est donn\'ee sous deux
formes: comme int\'egrale de la variation totale des projections de la
courbe dans les diverses directions et comme int\'egrale double du
nombre de rencontres de la courbe avec une droite quelconque du plan.
We give a general proof of the Cauchy formula about the length of a
plane curve. The formula is given in two ways: as the integral of the
variation of orthogonal projections of the curve, and as a double
integral of the number of intersections of the curve with an arbitrary
line of the plane.
Keywords:longueur, variation bornÃ©e, gÃ©omÃ©trie intÃ©grale Categories:28A75, 28A45 
