# The uniform invariant approximation property for compact groups

## TL;DR

This paper provides a proof of a refined version of the uniform invariant approximation property for compact non-commutative groups, extending previous results using Bourgain's approach.

## Contribution

It introduces a new proof of the refined uniform invariant approximation property for compact groups based on Bourgain's methodology.

## Key findings

- Established the refined uniform invariant approximation property for compact groups.
- Extended Bourgain's approach to non-commutative settings.
- Provided a new proof technique for the property.

## Abstract

In this short note we give a proof of the refined version of the uniform invariant approximation property for compact (non-commutative) groups following the Bourgain's approach.