Rademacher's theorem, named after Hans Rademacher, states that if U is an open subset of real n-dimensional space and f, mapping U into real m-dimensional space, is Lipschitz continuous, then f is differentiable almost everywhere in U, meaning the set of points where f fails to be differentiable has Lebesgue measure zero. Differentiability here means approximability by a linear map to first order, which in particular implies that all of f's coordinate-wise partial derivatives exist at almost every point. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Rademacher's Theorem (Wikipedia)
Sources
1. Rademacher's Theorem (Wikipedia)
In Branch: Analysis, Lead sentenceQuote, In Branch: Analysis, Lead sentence
In mathematical analysis, Rademacher's theorem, named after Hans Rademacher, states the following: If U is an open subset of Rn an
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.