"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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About the Author
Biography of Herbert Federer Herbert Federer was born on July 23, 1920, in Vienna. After emigrating to the US in 1938, he studied mathematics and physics at the University of California, Berkeley. Affiliated to Brown University, Providence since 1945, he is now Professor Emeritus there. The major part of Professor Federer's scientific effort has been directed to the development of the subject of Geometric Measure Theory, with its roots and applications in classical geometry and analysis, yet in the functorial spirit of modern topology and algebra. His work includes more than thirty research papers published between 1943 and 1986, as well as this book.
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29 of 31 people found the following review helpful:
5.0 out of 5 stars
The authoritative reference in the field.,
This review is from: Geometric Measure Theory (Classics in Mathematics) (Paperback)
First published in 1969 and initially intended as a reference for mature mathematicians and as a textbook for able students, this remarkable book constitutes the ultimate treatise on the subject still nowadays.It is written in an "economical" style, which means that you may well spend several hours in reading one single page (and there are 654 of them!). As a matter of fact, the author himself states in the preface that just chapter 2 is enough for a one-year graduate course. The contents are: 1 Grassmann Algebra. 2 General Measure Theory: Measures and measurable sets; Borel and Suslin sets; measurable functions; Lebesgue integration; linear functionals; product measures; invariant measures; covering theorems; derivates; Caratheodory's construction. 3 Rectifiability: Differentials and tangents; area and coarea of Lipschitzian maps; structure theory. 4 Homological Integration Theory: Differential forms and currents; deformations and compactness; slicing; homology groups; normal currents of dimension n in R^n. 5 Applicatios to the Calculus of Variations: Integrands and minimizing currents; regularity of solutions of certain differential equations; excess and smoothness; further results on area-minimizing currents. Each chapter could have been published as a separate monograph for they are +100 pages long! To read this book you must have a solid background in analysis, topology, differential geometry, and algebra, plus having mastered some introductory text on the subject, like Morgan's. Eventhough it is hard, the effort is worth it because it shows how to relate some concepts of analysis by means of algebraic or topological techniques. Includes extensive references though it lacks some motivation and explanations. Please take a look at the rest of my reviews (just click on my name above).
13 of 14 people found the following review helpful:
5.0 out of 5 stars
advise for those attempting Federer,
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This review is from: Geometric Measure Theory (Classics in Mathematics) (Paperback)
This is absolutely essential material to those wishing to apply the techniques of metric measure theory but is not a book to sit down and read. Instead buy both this book and Frank Morgan's "Geometric Measure Theory". Frank Morgan's book is an easy read for a graduate student with a semester of real analysis completed and is beautifully intuitive and has many illustrations. Even more convenient, it refers directly to the theorems in Federer's book by number so you can then go to Federer for the complete detailed proofs and the full general statements.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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homological integration theory, normed vectorspace, oriented tangent cone, parametric integrand, countable disjointed, semielliptic integrand, unit preserving algebra homomorphism, integral flat chains, constancy theorem, disjointed subfamilies, infer with the help, area minimizing currents, homotopy formulae, standard base vectors, dual orthonormal bases, real valued analytic functions, ellipticity bound, flat cochain, affine homotopy, covariant integral, oriented cone, general measure theory, analytic chain, area integrand, holomorphic chain Key Phrases - Capitalized Phrases (CAPs): (learn more)
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homological integration theory, normed vectorspace, oriented tangent cone, parametric integrand, countable disjointed, semielliptic integrand, unit preserving algebra homomorphism, integral flat chains, constancy theorem, disjointed subfamilies, infer with the help, area minimizing currents, homotopy formulae, standard base vectors, dual orthonormal bases, real valued analytic functions, ellipticity bound, flat cochain, affine homotopy, covariant integral, oriented cone, general measure theory, analytic chain, area integrand, holomorphic chain Key Phrases - Capitalized Phrases (CAPs): (learn more)
Using Fubini New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
100
books
cite this book:
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- Geometric Measure Theory, Third Edition: A Beginner's Guide by Frank Morgan in Front Matter, page 3, and page 207
- Almgren's Big Regularity Paper: Q-Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-Minimizing Rectifiable Currents Up to ... Scientific Monograph Series in Mathematics) by Frederick J., Jr. Almgren in Front Matter (1), Front Matter (2), and Back Matter
- Calculus of Variations and Partial Differential Equations: Topics on Geometrical Evolution Problems and Degree Theory (Universitext) by Luigi Ambrosio on page 101, and Back Matter
- Geometry V: Minimal Surfaces (Encyclopaedia of Mathematical Sciences) (v. 5) by Robert Osserman on page 219, and page 262
- Hausdorff Measures (Cambridge Mathematical Library) by C. A. Rogers in Front Matter (1), and Front Matter (2)
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