# The multidimensional truncated Moment Problem: Atoms, Determinacy, and Core Variety

## TL;DR

This paper explores the structure of the convex cone of moment functionals in finite-dimensional spaces, focusing on determinacy, atoms of measures, and core variety, advancing understanding of the multidimensional truncated moment problem.

## Contribution

It provides new insights into the structure of moment functionals, including their faces, atoms, and core variety, in the context of the multidimensional truncated moment problem.

## Key findings

- Characterization of the convex cone of moment functionals
- Analysis of the set of atoms of representing measures
- Investigation of the core variety and its properties

## Abstract

This paper is about the moment problem on a finite-dimensional vector space of continuous functions. We investigate the structure of the convex cone of moment functionals (supporting hyperplanes, exposed faces, inner points) and treat various important special topics on moment functionals (determinacy, set of atoms of representing measures, core variety).