# A tiling property for actions of amenable groups along Tempelman F{\o}lner sequences

## TL;DR

This paper proves a tiling property for actions of amenable groups along Tempelman F{\

## Contribution

It introduces a new combinatorial proof of the pointwise ergodic theorem for amenable groups using Tempelman F{\

## Key findings

- Establishes a tiling property that implies the pointwise ergodic theorem.
- Provides a short, combinatorial proof of the ergodic theorem for amenable groups.
- Validates the tiling property for actions along Tempelman F{\

## Abstract

We show that a certain tiling property (which directly implies the pointwise ergodic theorem) holds for pmp actions of amenable groups along increasing Tempelman F{\o}lner sequences, thus providing a short and combinatorial proof of the corresponding pointwise ergodic theorem.