CHAPTER I | **The integral in an abstract space ** | § 1. Introduction
§ 2. Terminology and notation
§ 3. Abstract space JT
§ 4. Additive classes of sets
§ 5. Additive functions of a set
§ 6. The variations of an additive function
§ 7. Measurable functions
§ 8. Elementary operations on measurable functions
§ 9. Measure
§ 10. Integral
§ 11. Fundamental properties of the integral
§ 12. Integration of sequences of functions
§ 13. Absolutely continuous additive functions of a set
§ 14. The Lebesgue decomposition of an additive function
§ 15. Change of measure |

CHAPTER II | **Caratheodory measure ** | § 1. Preliminary remarks
§ 2. Metrical space
§ 3. Continuous and semi-continuous functions
§ 4. Caratheodory measure
§ 5. The operation (A)
§ 6. Regular sets
§ 7. Bofel sets
§ 8. Length of a set
§ 9. Complete space |

CHAPTER III | **Functions of bounded variation and the Lebesgue-Stieltjes integral ** | § 1. Euclidean spaces
§ 2. Intervals and figures
§ 3. Functions of an interval
§ 4. Functions of an interval that are additive and of bounded variation
§ 5. Lebesgue-Stieltjes integral. Lebesgue integral and measure
§ 6. Measure defined by a non-negative additive function of an interval
§ 7. Theorems of Lusin and Vitali-Caratheodory
§ 8. Theorem of Fubini
§ 9. Fubini's theorem in abstract spaces
§ 10.Geometrical definition of the Lebesgue-Stieltjes integral
§ 11. Translations of sets
§ 12. Absolutely continuous functions of an interval
§ 13. Functions of a real variable
§ 14. Integration by parts |

CHAPTER IV | **Derivation of additive functions of a set and of an interval ** | § 1. Introduction
§ 2. Derivates of functions of a set and of an interval
§ 3. Vitali's Covering Theorem
§ 4. Theorems on measurability of derivates
§ 5. Lebesgue's Theorem
§ 6. Derivation of the indefinite integral
§ 7. The Lebesgue decomposition
§ 8. Rectifiable curves
§ 9. De la Vallee Poussin's theorem
§ 10. Points of density for a set
§ 11. Ward's theorems on derivation of additive functions of an interval
§ 12. A theorem of Hardy-Littlewood
§ 13. Strong derivation of the indefinite integral
§ 14. Symmetrical derivates
§ 15. Derivation in abstract spaces
§ 16. Torus space |

CHAPTER V | **Area of a surface z=F(x,y) ** | § 1. Preliminary remarks
§ 2. Area of a surface
§ 3. The Burkill integral
§ 4. Bounded variation and absolute continuity for functions of two variables
§ 5. The expressions of de Geocze
§ 6. Integrals of the expressions of de Geocze
§ 7. Rado's Theorem
§ 8. Tonelli's Theorem |

CHAPTER VI | **Major and minor functions ** | § 1. Introduction
§ 2. Derivation with respect to normal sequences of nets
§ 3. Major and minor functions
§ 4. Derivation with respect to binary sequences of nets
§ 5. Applications to functions of a complex variable
§ 6. The Perron integral
§ 7. Derivates of functions of a real variable
§ 8. The Perron-Stieltjes integral |

CHAPTER VII | **Functions of generalized bounded variation ** | § 1. Introduction
§ 2. A theorem of Lusin
§ 3. Approximate limits and derivatives
§ 4. Functions VB and VBG
§ 5. Functions AC and ACG
§ 6. Lusin's condition (N)
§ 7. Functions VB* and VBG*
§ 8. Functions AC* and ACG*
§ 9. Definitions of Denjoy-Lusin |

CHAPTER VIII | **Denjoy integrals ** | § 1. Descriptive definition of the Denjoy integrals
§ 2. Integration by parts
§ 3. Theorem of Hake-Alexandroff-Looman
§ 4. General notion of integral
§ 5. Constructive definition of the Denjoy integrals |

CHAPTER IX | **Derivates of functions of one or two real variables ** | § 1. Some elementary theorems
§ 2. Contingent of a set
§ 3. Fundamental theorems on the contingents of plane sets
§ 4. Denjoy's theorems
§ 5. Relative derivates
§ 6. The Banach conditions (Tx) and (T2)
§ 7. Three theorems of Banach
§ 8. Superpositions of absolutely continuous functions
§ 9. The condition (D)
§ 10. A theorem of Denjoy-Khintchine on approximate deriyates
§ 11. Approximate partial derivates of functions of two variables
§ 12. Total and approximate differentials
§ 13. Fundamental theorems on the contingent of a set in space
§ 14. Extreme differentials |

NOTE I | **S. BANACH ** | On Haar's measure |

NOTE II | **S. BANACH ** | The Lebesgue integral in abstract spaces |

Materiały redakcyjne | ** ** | Preface, errata, bibliography, general index, contents |