Federer Geometric Measure Theory Pdf |top| Jun 2026

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Review: Herbert Federer’s Geometric Measure Theory is a foundational, rigorous, and deeply detailed classic in the field. The text systematically develops the measure-theoretic and geometric underpinnings of surfaces and sets in Euclidean space, providing precise definitions, comprehensive theorems, and meticulous proofs. Federer’s exposition is terse and formal; readers benefit from a strong background in real analysis and differential geometry. Highlights include the theory of currents, rectifiability, and varifolds, along with powerful results like the structure of sets of finite perimeter and regularity theorems. The book is dense and demanding—ideal as a reference and for advanced graduate study, but challenging as a first introduction. Overall, an indispensable resource for researchers in geometric analysis and geometric measure theory. federer geometric measure theory pdf