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Geometric Measure Theory (Classics in Mathematics) Reprint of the 1st ed. Berlin, Heidelberg, New York 1969 Edition

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Herbert Federer (Author)
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4 out of 5 stars 4 customer reviews
ISBN-13: 978-3540606567
ISBN-10: 3540606564
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Product Details

  • Series: Classics in Mathematics
  • Paperback: 677 pages
  • Publisher: Springer; Reprint of the 1st ed. Berlin, Heidelberg, New York 1969 edition (January 5, 1996)
  • Language: English
  • ISBN-10: 3540606564
  • ISBN-13: 978-3540606567
  • Product Dimensions: 6.1 x 1.6 x 9.2 inches
  • Shipping Weight: 2.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #1,245,831 in Books (See Top 100 in Books)

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31 of 33 people found the following review helpful
The authoritative reference in the field.
By Bernardo Vargas on June 26, 2000
Format: 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).
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23 of 26 people found the following review helpful
advise for those attempting Federer
By Christina Sormani on October 26, 2006
Format: 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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2 of 2 people found the following review helpful
The book is encyclopedic, and has information (and proofs) ...
By Bill Houston on May 19, 2015
Format: Paperback Verified Purchase
The book is encyclopedic, and has information (and proofs) about all sorts of things related to integration and measure, particularly Hausdorff measure and other low-dimensional measures in higher-dimensional space. Federer strives for the utmost generality, which sometimes makes proofs much longer than the traditional ones (when there are traditional ones; many theorems seem to be completely original),. The book is very compactly written and so I had trouble filling in the gaps in many cases. There is a fairly large number of misprints and other minor errors.
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0 of 8 people found the following review helpful
abandon hope
By reader on October 12, 2014
Format: Paperback
abandon hope all ye who enter: this is the kind of thing that gives
math books a horrible reputation -- absolutely impenetrable to the non
initiate -- and written with what perversely seems almost to be a
deliberate attempt at obfuscation -- avoid like the plague
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