Geometric measure theory provides the framework to understand the structure of a crystal, a soap bubble cluster, or a universe. Measure Theory: A Beginner's Guide is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject.
1. Geometric Measure Theory
2. Measures
3. Lipschitz Functions and Rectifiable sets
4. Normal and Rectifiable Currents
5. The Compactness Theorem and the Existence of Area-Minimizing Surfaces
6. Examples of Area-Minimizing Surfaces
7. The Approximation Theorem
8. Survey of Regularity Results
9. Monotonicity and Oriented Tangent Cones
10. The Regularity of Area-Minimizing
etc.