# Singular Riesz measures on symmetric cones

## TL;DR

This paper explicitly characterizes a class of positive measures on symmetric cones via Laplace transforms, generalizing measures related to Wishart distributions, with implications for probability and statistics.

## Contribution

It provides a new explicit description of Riesz measures on symmetric cones, extending their application beyond classical Wishart distributions.

## Key findings

- Explicit description of Riesz measures on symmetric cones
- Generalization of Wishart distribution measures
- Potential applications in probability and statistical theory

## Abstract

In this paper, we give an explicitdescription of a class of positive measures on symmetric conesdefined by their Laplace transforms in the framework of the Rieszintegrals. This work is motivated by the importance of thesemeasures in probability theory and statistics sincethey represent a generalization of the measures generating the famous Wishart distributions.