Classics in Mathematics

By: Herbert Federer

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Paperback | 5 January 1996

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700 Pages

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24.13 x 15.88 x 3.18

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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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Introduction
Grassmann algebra
Tensor products	p. 8
Graded algebras	p. 11
The exterior algebra of a vectorspace	p. 13
Alternating forms and duality	p. 16
Interior multiplications	p. 21
Simple m-vectors	p. 23
Inner products	p. 27
Mass and comass	p. 38
The symmetric algebra of a vectorspace	p. 41
Symmetric forms and polynomial functions	p. 43
General measure theory
Measures and measurable sets	p. 51
Borrel and Suslin sets	p. 59
Measurable functions	p. 72
Lebesgue integration	p. 80
Linear functionals	p. 91
Product measures	p. 114
Invariant measures	p. 121
Covering theorems	p. 141
Derivates	p. 152
Caratheodory's construction	p. 169
Rectifiability
Differentials and tangents	p. 209
Area and coarea of Lipschitzian maps	p. 241
Structure theory	p. 287
Some properties of highly differentiable functions	p. 310
Homological integration theory
Differential forms and currents	p. 343
Deformations and compactness	p. 395
Slicing	p. 435
Homology groups	p. 463
Normal currents of dimension n in R[superscript n]	p. 474
Applications to the calculus of variations
Integrands and minimizing currents	p. 515
Regularity of solutions of certain differential equations	p. 532
Excess and smoothness	p. 565
Further results on area minimizing currents	p. 619
Bibliography	p. 655
Glossary of some standard notations	p. 669
List of basic notations defined in the text	p. 670
Index	p. 672
Table of Contents provided by Blackwell. All Rights Reserved.

Classics in Mathematics

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