bibkey: mityagin2015zeroset
authors: B. S. Mityagin
year: 2015
title: "The zero set of a real analytic function"
doi: 10.48550/arXiv.1512.07276
url: https://arxiv.org/abs/1512.07276v1
claim: "The zero set of a real-analytic function on a connected open domain of R^d that is not identically zero has Lebesgue measure zero."
strata_touched:
  - D5/S3/Quantum/Information/PauliRotationCriticalValues
license: citation-only
triage: anchor

Mityagin, the zero set of a real analytic function

B. S. Mityagin, The zero set of a real analytic function, arXiv:1512.07276v1 [math.CA] (22 December 2015; the only version).

Verified locator

DOI: 10.48550/arXiv.1512.07276. Primary version: https://arxiv.org/abs/1512.07276v1. Source: https://arxiv.org/pdf/1512.07276v1 (text read from the PDF), page 1, Proposition 0.

Source statements

Proposition 0, page 1: “Let A(x) be a real analytic function on (a connected open domain U of) R^d. If A is not identically zero, then its zero set F(A) := {x ∈ U : A(x) = 0} has a zero measure, i.e., mes_d F(A) = 0.”

The same page records that “Remark 5.23 in [Kuc15] and Lemma 1.2 in [Dan15] list possible approaches to the proof — from using Fubini’s theorem to Hironaka’s resolution of singularities.”