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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 maps

Nature: Exposition

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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 functions

Nature: Original

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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 laws

Nature: Original

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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 forms

Nature: Original

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Extension du théorème de Sazonov-Minlos d'après L.~Schwartz (Measure theory, Functional analysis)

Exposition of three notes by L.~Schwartz (

Comment: Self-contained and detailed exposition, possibly still useful

Keywords: Radonifying maps

Nature: Exposition

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V: 01, 1-16, LNM 191 (1971)

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 functions

Nature: Original

Retrieve article from Numdam

VI: 01, 1-34, LNM 258 (1972)

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 $

Comment: The results were announced in the note

Keywords: Decomposition of laws

Nature: Original

Retrieve article from Numdam

IX: 11, 285-293, LNM 465 (1975)

Quelques résultats de décomposabilité en algèbre linéaire et en algèbre quadratique aléatoires (Miscellanea)

It is shown that if a random quadratic form on $

Keywords: Independent random subspaces, Independent quadratic forms

Nature: Original

Retrieve article from Numdam