Item description for Geometric Measure Theory (Classics in Mathematics) by Herbert Federer...
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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Est. Packaging Dimensions: Length: 9.29" Width: 6.22" Height: 1.57" Weight: 2.25 lbs.
Release Date Jan 5, 1996
ISBN 3540606564 ISBN13 9783540606567
Availability 78 units. Availability accurate as of Oct 26, 2016 11:38.
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Reviews - What do customers think about Geometric Measure Theory (Classics in Mathematics)?
advise for those attempting Federer Oct 27, 2006
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.
The authoritative reference in the field. Jun 26, 2000
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).