III: 01, 1-23, LNM 88 (1969)
ARTZNER, Philippe
Extension du théorème de Sazonov-Minlos d'après L.~Schwartz (
Measure theory,
Functional analysis)
Exposition of three notes by L.~Schwartz (
CRAS 265, 1967 and
266, 1968) showing that some classes of maps between spaces $\ell^p$ and $\ell^q$ transform Gaussian cylindrical measures into Radon measures. The result turns out to be an extension of Minlos' theorem
Comment: Self-contained and detailed exposition, possibly still useful
Keywords: Radonifying mapsNature: Exposition
Retrieve article from Numdam
V: 01, 1-16, LNM 191 (1971)
ARTZNER, Philippe
Fonctions caractéristiques et mesures planes invariantes par rotation (
Miscellanea)
A study of the class of probability measures on the line which are projections of a measure on the plane invariant by rotation
Keywords: Characteristic functionsNature: Original Retrieve article from Numdam
VI: 01, 1-34, LNM 258 (1972)
ARTZNER, Philippe
Echantillons et couples indépendants de points aléatoires portés par une surface convexe (
Independence)
The general problem is to find conditions under which a convolution equation $\mu{*}\mu=\mu'{*}\mu''$ in $
R^n$ implies that $\mu'=\mu''=\mu$. It is shown here that the result is true if the measures are carried by a convex surface which is not too flat
Comment: The results were announced in the note
C. R. Acad. Sci., 272, 1971
Keywords: Decomposition of lawsNature: Original Retrieve article from Numdam
IX: 11, 285-293, LNM 465 (1975)
ARTZNER, Philippe
Quelques résultats de décomposabilité en algèbre linéaire et en algèbre quadratique aléatoires (
Miscellanea)
It is shown that if a random quadratic form on $
R^4$ is a.s. of rank 3 and has an absolutely continuous law, then its law is indecomposable. To prove this, it is shown that the sum of two independent planes in $
R^4$ cannot at the same time be a.s. a hyperplane and have an absolutely continuous law (with respect to the natural measure for hyperplanes)
Keywords: Independent random subspaces,
Independent quadratic formsNature: Original Retrieve article from Numdam
