# A note on the convergence of almost minimal sets

## TL;DR

This paper demonstrates that for almost minimal sets, Hausdorff convergence and varifold convergence are equivalent, clarifying the relationship between these two notions of convergence in geometric measure theory.

## Contribution

It establishes the equivalence of Hausdorff and varifold convergence specifically for the class of almost minimal sets, a previously unclear relationship.

## Key findings

- Hausdorff and varifold convergence coincide for almost minimal sets
- Provides a clearer understanding of convergence in geometric measure theory
- Enhances the theoretical foundation for studying minimal and almost minimal sets

## Abstract

In this paper, we will show that Hausdorff convergence and varifold convergence coincide on the class of almost minimal sets.