# Arbitrary functional Glivenko-Cantelli classes and applications to different types of dependence

## TL;DR

This paper develops a broad theoretical framework for Glivenko-Cantelli classes applicable to various dependent stationary processes, extending classical results and comparing with existing literature.

## Contribution

It introduces a general approach to establish functional Glivenko-Cantelli classes for arbitrary stationary processes using entropy numbers and a strong law of large numbers.

## Key findings

- Established GC classes for diverse dependence structures
- Compared new results with existing literature
- Extended classical empirical process theory to dependent data

## Abstract

Using a general strong law of large number proved by Sangar\'e and Lo (2015) and the entropy numbers, we provide functional Glivenko-Cantelli (GC) classes for arbitrary stationary real-valued random variables (rrv's). Next, the general results are particularized for different types of dependence (association, $\phi$-mixing, in particular) and compared with available results in the literature.