# On a metric on the space of monetary risk measures

## TL;DR

This paper introduces a new metric for the space of monetary risk measures that aligns with point-wise convergence and extends existing metrics on compact sets.

## Contribution

It proposes a novel metric on monetary risk measures that captures convergence behavior and extends previous metrics on compact spaces.

## Key findings

- The metric generates the point-wise convergence topology.
- It extends the metric on the initial compactum.
- Provides a framework for analyzing convergence of risk measures.

## Abstract

We introduce a metric on the space of monetary risk measure, which generates the point-wise convergence topology and extends the metric on the initial compactum.