Rev. ed. of: Real analysis. 2nd ed. 1983.

8. Product Measures and Integration on a Product Space. 9. The Lebesgue Integral in R[superscript p] -- Ch. VII. Duality and Representation Theorems. 1. The Hilbert Space L[superscript 2](mu). 2. Duality Between [actual symbol not reproducible]. 3. Complex and Vectorial Measures. 4. Complex or Vectorial Measures and Duality. 5. The L[superscript p] Spaces, [actual symbol not reproducible]. 6. The Law of Large Numbers -- Ch. VIII. Some Applications of Integration. 1. Convolution. 2. Continuity and Differentiation Under the Integral Sign. 3. Dirac Sequences. 4. The Schwartz Space and Fourier Transform. 5. The Fourier Inversion Formula. 6. The Poisson Summation Formula. 7. An Example of Fourier Transform Not in the Schwartz Space -- Ch. IX. Integration and Measures on Locally Compact Spaces. 1. Positive and Bounded Functionals on C[subscript c](X). 2. Positive Functionals as Integrals. 3. Regular Positive Measures. 4. Bounded Functionals as Integrals.

5. Localization of a Measure and of the Integral. 6. Product Measures on Locally Compact Spaces -- Ch. X. Riemann-Stieltjes Integral and Measure. 1. Functions of Bounded Variation and the Stieltjes Integral. 2. Applications to Fourier Analysis -- Ch. XI. Distributions. 1. Definition and Examples. 2. Support and Localization. 3. Derivation of Distributions. 4. Distributions with Discrete Support -- Ch. XII. Integration on Locally Compact Groups. 1. Topological Groups. 2. The Haar Integral, Uniqueness. 3. Existence of the Haar Integral. 4. Measures on Factor Groups and Homogeneous Spaces -- Ch. XIII. Differential Calculus. 1. Integration in One Variable. 2. The Derivative as a Linear Map. 3. Properties of the Derivative. 4. Mean Value Theorem. 5. The Second Derivative. 6. Higher Derivatives and Taylor's Formula. 7. Partial Derivatives. 8. Differentiating Under the Integral Sign. 9. Differentiation of Sequences -- Ch. XIV. Inverse Mappings and Differential Equations.

1. The Inverse Mapping Theorem. 2. The Implicit Mapping Theorem. 3. Existence Theorem for Differential Equations. 4. Local Dependence on Initial Conditions. 5. Global Smoothness of the Flow -- Ch. XV. The Open Mapping Theorem, Factor Spaces, and Duality. 1. The Open Mapping Theorem. 2. Orthogonality. 3. Applications of the Open Mapping Theorem -- Ch. XVI. The Spectrum. 1. The Gelfand-Mazur Theorem. 2. The Gelfand Transform. 3. C*-Algebras -- Ch. XVII. Compact and Fredholm Operators. 1. Compact Operators. 2. Fredholm Operators and the Index. 3. Spectral Theorem for Compact Operators. 4. Application to Integral Equations -- Ch. XVIII. Spectral Theorem for Bounded Hermitian Operators. 1. Hermitian and Unitary Operators. 2. Positive Hermitian Operators. 3. The Spectral Theorem for Compact Hermitian Operators. 4. The Spectral Theorem for Hermitian Operators. 5. Orthogonal Projections. 6. Schur's Lemma. 7. Polar Decomposition of Endomorphisms. 8. The Morse-Palais Lemma.

Ch. XIX. Further Spectral Theorems. 1. Projection Functions of Operators. 2. Self-Adjoint Operators. 3. Example: The Laplace Operator in the Plane -- Ch. XX. Spectral Measures. 1. Definition of the Spectral Measure. 2. Uniqueness of the Spectral Measure: the Titchmarsh-Kodaira Formula. 3. Unbounded Functions of Operators. 4. Spectral Families of Projections. 5. The Spectral Integral as Stieltjes Integral -- Ch. XXI. Local Integration of Differential Forms. 1. Sets of Measure 0. 2. Change of Variables Formula. 3. Differential Forms. 4. Inverse Image of a Form. 5. Appendix -- Ch. XXII. Manifolds. 1. Atlases, Charts, Morphisms. 2. Submanifolds. 3. Tangent Spaces. 4. Partitions of Unity. 5. Manifolds with Boundary. 6. Vector Fields and Global Differential Equations -- Ch. XXIII. Integration and Measures on Manifolds. 1. Differential Forms on Manifolds. 2. Orientation. 3. The Measure Associated with a Differential Form. 4. Stokes' Theorem for a Rectangular Simplex.

5. Stokes' Theorem on a Manifold. 6. Stokes' Theorem with Singularities.