# Fekete's lemma for componentwise subadditive functions of two or more real variables

## TL;DR

This paper extends Fekete's lemma to functions of multiple variables that are subadditive in each variable separately, demonstrating boundedness on bounded sets and generalizing classical results.

## Contribution

It introduces a multivariable analogue of Fekete's lemma for componentwise subadditive functions, expanding the classical one-variable case and previous partial results.

## Key findings

- Proves an analogue of Fekete's lemma for multivariable functions
- Shows such functions are bounded on bounded subsets
- Extends classical subadditivity results to multiple variables

## Abstract

We prove an analogue of Fekete's subadditivity lemma for functions of several real variables which are subadditive in each variable taken singularly. This extends both the classical case for subadditive functions of one real variable, and a result in a previous paper by the author. While doing so, we prove that the functions with the property mentioned above are bounded in every closed and bounded subset of their domain. The arguments follows those of Chapter 6 in E. Hille's 1948 textbook.