Sobolev spaces on metric measure spaces : an approach based on upper gradients

Preface 1. Introduction 2. Review of basic functional analysis 3. Lebesgue theory of Banach space-valued functions 4. Lipschitz functions and embeddings 5. Path integrals and modulus 6. Upper gradients 7. Sobolev spaces 8. Poincare inequalities 9. Consequences of Poincare inequalities 10. Other definitions of Sobolev-type spaces 11. Gromov-Hausdorff convergence and Poincare inequalities 12. Self-improvement of Poincare inequalities 13. An Introduction to Cheeger's differentiation theory 14. Examples, applications and further research directions References Notation index Subject index.