Surface Area. (AM-35), Volume 35

CONTENTS\nPREFACE\nCHAPTER I. INTRODUCTORY CONSIDERATIONS\n	§1. The Main Theorems\n	§2. Some Basic Definitions for Curves\n	§3. Some Definitions for Non-Parametric Surfaces\n	§4. The Example of Schwarz and Peano\nCHAPTER II. LEBESGUE AREA\n	§5. The Lebesgue Area L\n	§6. Some Alternate Definitions of Lebesgue Area\n	§7. Some Critical Considerations on Area\nCHAPTER III. THE GEÖCZE AREAS V AND U AND THE PEANO AREA P\n	§8. The Topological Index\n	§9. The Geocze and Peano Areas V, U, P\n	§10. Continuous Mappings and Semicontinuous Collections\n	§11. Some Properties of the Euclidean Plane E2\nCHAPTER IV. BV AND AC PLANE MAPPINGS\n	§12. BV Plane Mappings\n	§13. AC Plane Mappings\n	§14. Local Properties of Plane Mappings\n	§15. A Characterization of AC Plane Mappings\nCHAPTER V. THE FIRST THEOREM\n	§16. An Analytical Property of Continuous Mappings\n	§17. Some Properties of Homotopy for Continuous Curves in E3\n	§18. The First Theorem\nCHAPTER VI. THE CAVALIERI INEQUALITY\n	§19. On the Boundary of Open Sets (Carathéodory Theory)\n	§20. Contours of a Continuous Surface and the Cavalieri Inequality\nCHAPTER VII. IDENTIFICATION OF LEBESGUE, GEÖCZE, PEANO AREAS\n	§21. The Equality V = U\n	§22. Some Limit Theorems for the Functions U and V\n	§23. Some Analytical Properties of Continuous Mappings\n	§24. The Equality V = L = P\n	§25. The Lebesgue Area as a Measure Function\nCHAPTER VIII. GEOMETRICAL PROPERTIES AND THE SECOND THEOREM\n	§26. Regular Approximate Differentials\n	§27. Interval Functions\n	§28. Generalized Jacobians\n	§29. Formulas for the Transformation of Areas and Double Integrals\n	§30. The Second Theorem\nCHAPTER IX. THE REPRESENTATION PROBLEM\n	§31. Fréchet Equivalence\n	§32. Mean Value Integrals of L-Integrable Functions\n	§33. Some Particular Types of Surfaces\n	§34. Representation Theorems for Non-Degenerate Surfaces\nCHAPTER X. THE REPRESENTATION OF GENERAL SURFACES AND THE THIRD THEOREM\n	§35. Generalized Conformal Representations\n	§36. A Retraction Process for Surfaces\n	§37. Representation of General Surfaces, The Third Theorem\nAPPENDIX A. A DIRECT PROOF OF A PROPERTY OF CONTINUOUS SURFACES\nAPPENDIX B. WEIERSTRASS INTEGRAL OVER A SURFACE\nBIBLIOGRAPHY\nSPECIAL SIGNS AND ABBREVIATIONS