Geometric measure theory
From the reviews: ..." Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst.""Bulletin of the London Mathematical Society"
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algebra analytic apply associated assume Borel regular Borel set Borel subset bounded cartesian product characteristic function choose class oo compact subset compute conclude construct continuous convex Corollary corresponding countable countable family covariant Daniell integral define diam differential form dimensional submanifold disjoint elliptic equals equation exists finite flat chains follows formula function mapping Geometric Measure Theory Haar Hausdorff Hausdorff measure hence homomorphism hypothesis implies inequality infer inner product integrand of degree isomorphism Lemma linear map Lipschitz Lipschitzian map locally Lipschitzian measurable function measurable set metric space minimizing with respect Moreover neighborhood nonempty normed observe obtain open set open subset oriented orthogonal orthonormal parametric integrand positive integer positive numbers Proof proposition prove Radon measure real number Recalling regular measure replaced satisfy the conditions sequence submanifold of class summable Suppose Suslin subset Theorem topology univalent vector vectorfield vectorspace vectorsubspace xeRm