| Preface to the First Edition | p. xiii |
| Preface to the Second Edition | p. xvii |
| Notations | p. xix |
| Measure Spaces | p. 1 |
| Introduction | p. 1 |
| Measure on a [sigma]-algebra of Sets | p. 3 |
| [sigma]-algebra of Sets | p. 3 |
| Limits of Sequences of Sets | p. 4 |
| Generation of [sigma]-algebras | p. 6 |
| Borel [sigma]-algebras | p. 9 |
| Measure on a [sigma]-algebra | p. 11 |
| Measures of a Sequence of Sets | p. 14 |
| Measurable Space and Measure Space | p. 17 |
| Measurable Mapping | p. 19 |
| Induction of Measure by Measurable Mapping | p. 22 |
| Outer Measures | p. 28 |
| Construction of Measure by Means of Outer Measure | p. 28 |
| Regular Outer Measures | p. 32 |
| Metric Outer Measures | p. 34 |
| Construction of Outer Measures | p. 37 |
| Lebesgue Measure on R | p. 41 |
| Lebesgue Outer Measure on R | p. 41 |
| Some Properties of the Lebesgue Measure Space | p. 45 |
| Existence of Non Lebesgue Measurable Sets | p. 49 |
| Regularity of Lebesgue Outer Measure | p. 51 |
| Lebesgue Inner Measure on R | p. 57 |
| Measurable Functions | p. 70 |
| Measurability of Functions | p. 70 |
| Operations with Measurable Functions | p. 74 |
| Equality Almost Everywhere | p. 78 |
| Sequence of Measurable Functions | p. 79 |
| Continuity and Borel and Lebesgue Measurability of Functions on R | p. 83 |
| Cantor Ternary Set and Cantor-Lebesgue Function | p. 85 |
| Completion of Measure Space | p. 95 |
| Complete Extension and Completion of a Measure Space | p. 95 |
| Completion of the Borel Measure Space to the Lebesgue Measure Space | p. 98 |
| Convergence a.e. and Convergence in Measure | p. 100 |
| Convergence a.e. | p. 100 |
| Almost Uniform Convergence | p. 104 |
| Convergence in Measure | p. 107 |
| Cauchy Sequences in Convergence in Measure | p. 112 |
| Approximation by Step Functions and Continuous Functions | p. 115 |
| The Lebesgue Integral | p. 127 |
| Integration of Bounded Functions on Sets of Finite Measure | p. 127 |
| Integration of Simple Functions | p. 127 |
| Integration of Bounded Functions on Sets of Finite Measure | p. 131 |
| Riemann Integrability | p. 140 |
| Integration of Nonnegative Functions | p. 152 |
| Lebesgue Integral of Nonnegative Functions | p. 152 |
| Monotone Convergence Theorem | p. 154 |
| Approximation of the Integral by Truncation | p. 162 |
| Integration of Measurable Functions | p. 169 |
| Lebesgue Integral of Measurable Functions | p. 169 |
| Convergence Theorems | p. 178 |
| Convergence Theorems under Convergence in Measure | p. 182 |
| Approximation of the Integral by Truncation | p. 183 |
| Translation and Linear Transformation in the Lebesgue Integral on R | p. 189 |
| Integration by Image Measure | p. 193 |
| Signed Measures | p. 202 |
| Signed Measure Spaces | p. 202 |
| Decomposition of Signed Measures | p. 208 |
| Integration on a Signed Measure Space | p. 217 |
| Absolute Continuity of a Measure | p. 224 |
| The Radon-Nikodym Derivative | p. 224 |
| Absolute Continuity of a Signed Measure Relative to a Positive Measure | p. 225 |
| Properties of the Radon-Nikodym Derivative | p. 236 |
| Differentiation and Integration | p. 245 |
| Monotone Functions and Functions of Bounded Variation | p. 245 |
| The Derivative | p. 245 |
| Differentiability of Monotone Functions | p. 251 |
| Functions of Bounded Variation | p. 261 |
| Absolutely Continuous Functions | p. 270 |
| Absolute Continuity | p. 270 |
| Banach-Zarecki Criterion for Absolute Continuity | p. 273 |
| Singular Functions | p. 276 |
| Indefinite Integrals | p. 276 |
| Calculation of the Lebesgue Integral by Means of the Derivative | p. 287 |
| Length of Rectifiable Curves | p. 298 |
| Convex Functions | p. 308 |
| Continuity and Differentiability of a Convex Function | p. 308 |
| Monotonicity and Absolute Continuity of a Convex Function | p. 317 |
| Jensen's Inequality | p. 320 |
| The Classical Banach Spaces | p. 323 |
| Normed Linear Spaces | p. 323 |
| Banach Spaces | p. 323 |
| Banach Spaces on R[superscript k] | p. 326 |
| The Space of Continuous Functions C([a, b]) | p. 329 |
| A Criterion for Completeness of a Normed Linear Space | p. 331 |
| Hilbert Spaces | p. 333 |
| Bounded Linear Mappings of Normed Linear Spaces | p. 334 |
| Baire Category Theorem | p. 344 |
| Uniform Boundedness Theorems | p. 347 |
| Open Mapping Theorem | p. 350 |
| Hahn-Banach Extension Theorems | p. 357 |
| Semicontinuous Functions | p. 370 |
| The L[superscript p] Spaces | p. 376 |
| The L[superscript p] Spaces for p [set membership] (0, [infinity] | p. 376 |
| The Linear Spaces L[superscript p] for p [set membership] [1, infinity] | p. 379 |
| The L[superscript p] Spaces for p [set membership] [1, infinity]) | p. 384 |
| The Space L[superscript infinity]] | p. 393 |
| The L[superscript p] Spaces for p [set membership] (0, 1) | p. 401 |
| Extensions of Holder's Inequality | p. 406 |
| Relation among the L[superscript p] Spaces | p. 412 |
| The Modified L[superscript p] Norms for L[superscript p] Spaces with p [set membership] [1, infinity] | p. 412 |
| Approximation by Continuous Functions | p. 414 |
| L[superscript p] Spaces with p [set membership] (0, 1] | p. 417 |
| The l[superscript p] Spaces | p. 422 |
| Bounded Linear Functionals on the L[superscript p] Spaces | p. 429 |
| Bounded Linear Functionals Arising from Integration | p. 429 |
| Approximation by Simple Functions | p. 432 |
| A Converse of Holder's Inequality | p. 434 |
| Riesz Representation Theorem on the L[superscript p] Spaces | p. 437 |
| Integration on Locally Compact Hausdorff Space | p. 445 |
| Continuous Functions on a Locally Compact Hausdorff Space | p. 445 |
| Borel and Radon Measures | p. 450 |
| Positive Linear Functionals on C[subscript c](X) | p. 455 |
| Approximation by Continuous Functions | p. 463 |
| Signed Radon Measures | p. 467 |
| The Dual Space of C(X) | p. 471 |
| Extension of Additive Set Functions to Measures | p. 481 |
| Extension of Additive Set Functions on an Algebra | p. 481 |
| Additive Set Function on an Algebra | p. 481 |
| Extension of an Additive Set Function on an Algebra to a Measure | p. 486 |
| Regularity of an Outer Measure Derived from a Countably Additive Set Function on an Algebra | p. 486 |
| Uniqueness of Extension of a Countably Additive Set Function on an Algebra to a Measure | p. 489 |
| Approximation to a [sigma]-algebra Generated by an Algebra | p. 491 |
| Outer Measure Based on a Measure | p. 494 |
| Extension of Additive Set Functions on a Semialgebra | p. 496 |
| Semialgebras of Sets | p. 496 |
| Additive Set Function on a Semialgebra | p. 498 |
| Outer Measures Based on Additive Set Functions on a Semialgebra | p. 502 |
| Lebesgue-Stieltjes Measure Spaces | p. 505 |
| Lebesgue-Stieltjes Outer Measures | p. 505 |
| Regularity of the Lebesgue-Stieltjes Outer Measures | p. 509 |
| Absolute Continuity and Singularity of a Lebesgue-Stieltjes Measure | p. 511 |
| Decomposition of an Increasing Function | p. 519 |
| Product Measure Spaces | p. 527 |
| Existence and Uniqueness of Product Measure Spaces | p. 527 |
| Integration on Product Measure Space | p. 531 |
| Completion of Product Measure Space | p. 543 |
| Convolution of Functions | p. 547 |
| Some Related Theorems | p. 587 |
| Measure and Integration on the Euclidean Space | p. 597 |
| Lebesgue Measure Space on the Euclidean Space | p. 597 |
| Lebesgue Outer Measure on the Euclidean Space | p. 597 |
| Regularity Properties of Lebesgue Measure Space on R[superscript n] | p. 602 |
| Approximation by Continuous Functions | p. 605 |
| Lebesgue Measure Space on R[superscript n] as the Completion of a Product Measure Space | p. 609 |
| Translation of the Lebesgue Integral on R[superscript n] | p. 610 |
| Linear Transformation of the Lebesgue Integral on R[superscript n] | p. 612 |
| Differentiation on the Euclidean Space | p. 620 |
| The Lebesgue Differentiation Theorem on R[superscript n] | p. 620 |
| Differentiation of Set Functions with Respect to the Lebesgue Measure | p. 632 |
| Differentiation of the Indefinite Integral | p. 634 |
| Density of Lebesgue Measurable Sets Relative to the Lebesgue Measure | p. 635 |
| Signed Borel Measures on R[superscript n] | p. 641 |
| Differentiation of Borel Measures with Respect to the Lebesgue Measure | p. 643 |
| Change of Variable of Integration on the Euclidean Space | p. 649 |
| Change of Variable of Integration by Differentiable Transformations | p. 649 |
| Spherical Coordinates in R[superscript n] | p. 661 |
| Integration by Image Measure on Spherical Surfaces | p. 667 |
| Hausdorff Measures on the Euclidean Space | p. 675 |
| Hausdorff Measures | p. 675 |
| Hausdorff Measures on R[superscript n] | p. 675 |
| Equivalent Definitions of Hausdorff Measure | p. 680 |
| Regularity of Hausdorff Measure | p. 686 |
| Hausdorff Dimension | p. 689 |
| Transformations of Hausdorff Measures | p. 694 |
| Hausdorff Measure of Transformed Sets | p. 694 |
| 1-dimensional Hausdorff Measure | p. 699 |
| Hausdorff Measure of Jordan Curves | p. 700 |
| Hausdorff Measures of Integral and Fractional Dimensions | p. 705 |
| Hausdorff Measure of Integral Dimension and Lebesgue Measure | p. 705 |
| Calculation of the n-dimensional Hausdorff Measure of a Unit Cube in R[superscript n] | p. 707 |
| Transformation of Hausdorff Measure of Integral Dimension | p. 713 |
| Hausdorff Measure of Fractional Dimension | p. 718 |
| Bibliography | p. 727 |
| Index | p. 729 |
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