Geometric Measure TheoryFrom 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 |
Contents
| 1 | |
Approximation by closed subsets | 59 |
Existence and uniqueness of invariant integrals | 123 |
The general construction | 169 |
CHAPTER THREE | 207 |
CHAPTER FOUR | 341 |
CHAPTER FIVE | 513 |
| 655 | |
| 664 | |
Glossary of some standard notations | 669 |
| 673 | |
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Common terms and phrases
a₁ algebra analytic apply assume b₁ Bdry Borel set Borel subset characteristic function choose Clos compact subset compute conclude construct convex Corollary corresponding countable countable family covariant currents Daniell integral define diam differential form dimensional submanifold disjoint dL¹ e₁ equation exists finite flat chains follows formula Geometric Measure Theory Haar Hausdorff Hausdorff measure hence holomorphic implies induction inequality infer integer integrand Lemma lim sup linear map Lipschitzian map locally Lipschitzian measurable function measurable set metric space Moreover neighborhood nonempty observe obtain open subset oriented positive integer positive numbers Proof prove Radon measure real valued rectifiable replaced S₁ satisfy the conditions sequence submanifold of class Suppose Theorem univalent v₁ vector vectorfield vectorspace vectorsubspace verify w₁ Σ Σ