Notes on SU(2) invariant absolutely continuous probability measures

TL;DR

This paper investigates the properties of $SU(2)$-invariant probability measures on convex cones in $C^2$, establishing measure independence using Haar measure theory for compact groups.

Contribution

It proves a measure independence property for $SU(2)$-invariant distributions on convex cones in $C^2$, leveraging Haar measure existence.

Findings

Establishes measure independence for $SU(2)$-invariant measures.

Utilizes Haar measure for compact groups to prove invariance properties.

Provides theoretical foundation for invariant probability measures in complex vector spaces.

Abstract

A measure independence property of Lebesgue measurable convex cones of $\mathbb{C}^2$, for $SU(2)$ transformations invariant continuous probability joint distributions over $\mathbb{C}^2$, will be proved using the existence of the Haar probability measure for compact Hausdorff topological groups.