The Zero Set of a Real Analytic Function
By Boris Mityagin. Mathematical Notes, 2015
267 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c6c9b14a1e3f21bd756318062dce90ddb247738d
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Demystifying MMD GANs (2018, unknown): “This result is shown e.g. as Proposition 0 of Mityagin (2015).”
- The loss surface and expressivity of deep convolutional neural networks (2017, background): “Lemma A.2 Nguyen (2015); Mityagin (2015) If f : R n → R is a real analytic function which is not identically zero then the set { x ∈ R n | f ( x ) = 0 } has Lebesgue measure zero.”
- Optimization Landscape and Expressivity of Deep CNNs (2017, background): “Lemma A.1 (Nguyen, 2015; Mityagin, 2015) If f : R n → R is a real analytic function which is not identically zero then the set { x ∈ R n | f ( x ) = 0 } has Lebesgue measure zero.”