*Frontmatter, pg. i*PREFACE, pg. vii*CONTENTS, pg. ix*CHAPTER I. INTRODUCTORY- CONSIDERATIONS, pg. 1*CHAPTER II. LEBESGUE AREA, pg. 27*CHAPTER III. THE GEOCZE AREAS V AND U AND THE PEANO AREA P, pg. 83*CHAPTER IV. BV AND AC PLANE MAPPINGS, pg. 173*CHAPTER V. THE FIRST THEOREM, pg. 242*CHAPTER VI. THE CAVALIERI INEQUALITY, pg. 298*CHAPTER VII. IDENTIFICATION OF LEBESGUE, GEOCZE, PEANO AREAS, pg. 331*CHAPTER VIII. GEOMETRICAL PROPERTIES AND THE SECOND THEOREM, pg. 407*CHAPTER IX. THE REPRESENTATION PROBLEM, pg. 449*CHAPTER X. THE REPRESENTATION OF GENERAL SURFACES AND THE THIRD THEOREM, pg. 487*APPENDIX A. A DIRECT PROOF OF A PROPERTY OF CONTINUOUS SURFACES, pg. 550*APPENDIX B. WEIERSTRASS INTEGRAL OVER A SURFACE, pg. 564*BIBLIOGRAPHY, pg. 577*SPECIAL SIGNS AND ABBREVIATIONS, pg. 595*Backmatter, pg. 598
