This book aims to fill the need for a comprehensive treatise on geo-metric measure theory. It contains a detailed exposition leading from the foundations of the theory to the most recent discoveries, including many results not previously published. It is intended both as a reference book for mature mathematicians and as a textbook for able students. The material of Chapter 2 can be covered in a first year graduate course on real analysis. Study of the later chapters is suitable preparation for re-search. Some knowledge of elementary set theory, topology, linear algebra and commutative ring theory is prerequisite for reading this book, but the treatment is selfcontained with regard to all those topics in multilinear algebra, analysis, differential geometry and algebraic topology which occur.

本书为英文版。

Introduction

Chapter One Grassmann algebra

 1.1. Tensor products

 1.2. Graded algebras

 1.3. The exterior algebra of a vectorspace

 1.4. Alternating forms and duality

 1.5. Interior multiplications

 1.6. Simple m-vectors

 1.7. Inner products

 1.8. Mass and comass

 1.9. The symmetric algebra of a vectorspace

 1.10. Symmetric forms and polynomial functions

CHAPTER TWO General measure theory

CHAPTER THREE Rectifiability

CHAPTER FOUR Homological integration theory

CHAPTER FIVE Applications to the calculus of variations

Bibliography

Glossary of some standrd notations

List of basic notations defined in the text

Index