The Zero Set of a Real Analytic Function

TL;DR

This paper provides a concise proof that the zero set of any nontrivial real-analytic function in multi-dimensional space has measure zero, highlighting a fundamental property of such functions.

Contribution

It offers a brief, clear proof of the measure-zero property of zero sets for nontrivial real-analytic functions, simplifying existing arguments.

Findings

Zero set of nontrivial real-analytic functions has measure zero

The proof is concise and accessible

Reinforces fundamental properties of real-analytic functions

Abstract

A brief proof of the statement that the zero-set of a nontrivial real-analytic function in $d$-dimensional space has zero measure is provided.