Measure theory and integration / M.M. Rao.

Format:

Book

Author/Creator:

Rao, M. M. (Malempati Madhusudana), 1929-

Contributor:

Alumni and Friends Memorial Book Fund.

Series:

Monographs and textbooks in pure and applied mathematics ; 265.

Monographs and textbooks in pure and applied mathematics ; 265

Language:

English

Subjects (All):

Measure theory.

Integrals, Generalized.

Physical Description:

xix, 761 pages ; 24 cm.

Edition:

Second edition, revised and expanded.

Place of Publication:

New York : Marcel Dekker, [2004]

Contents:

1.2. The Space R[superscript n] as a Model 4

1.3. Abstraction of the Salient Features 14

2. Measurability and Measures 21

2.1. Measurability and Class Properties 21

2.2. The Lebesgue Outer Measure and the Caratheodory Process 30

2.3. Extensions of Measures to Larger Classes 67

2.4. Distinction between Finite and Infinite Measures 86

2.5. Metric Outer Measures 92

2.6. Lebesgue-Stieltjes Measures 99

3. Measurable Functions 110

3.1. Definition and Basic Properties 110

3.2. Measurability with Measures and Convergence 120

3.3. Image Measures and Vague Convergence 136

4. Classical Integration 147

4.1. The Abstract Lebesgue Integral 147

4.2. Integration of Nonmeasurable Functions 163

4.3. The Lebesgue Limit Theorems 171

4.4. The Vitali-Hahn-Saks Theorem and Signed Measures 191

4.5. The L[superscript p]-spaces 203

4.6. The Four Basic Theorems of Banach Spaces 238

5. Differentiation and Duality 255

5.1. Variations of Set Functions and the Hahn Decomposition 255

5.2. Absolute Continuity and Complete Monotonicity of Functions 268

5.3. The Radon-Nikodym Theorem: Sigma-Finite Case 296

5.4. The Radon-Nikodym Theorem: General Case 320

5.5. Duality of L[superscript p]-spaces and Conditional Expectations 330

6. Product Measures and Integrals 364

6.1. Basic Definitions and Properties 364

6.2. The Fubini-Stone and Tonelli Theorems 381

6.3. Remarks on Non-Cartesian Products 398

6.4. Infinite Product Measures 405

6.5. Two Applications of Infinite Products 437

7. Nonabsolute Integration 452

7.1. Nonabsolute Integration on the Line 453

7.2. Product Spaces and P-Integration 488

7.3. Vector Integration 502

7.4. Boundedness Principles for Nonabsolute Integration 517

7.5. Some Complements 549

8. Capacity Theory and Integration 563

8.1. Preliminaries on Analytic Sets 563

8.2. Capacity: A Construction and Choquet's Theorem 570

8.3. Application to the Daniell Integral 585

9. The Lifting Theorem 599

9.1. The problem, Motivation, and Preliminaries 599

9.2. Existence Proof for the Lifting Map 611

9.3. Topologies Induced by Lifting and Related Concepts 622

10. Topological Measures 631

10.2. Regularity of Measures 639

10.3. Local Functionals and the Riesz-Markov Theorem 667

10.4. Haar Measures 687

11. Some Complements and Applications 703

11.1. Lattice and Homomorphism Properties 703

11.2. Some Applications of the Stone Isomorphism Theorem 713

11.3. Remarks on Topology of a Group Through Measure 729.

Notes:

1st ed. (1987) pub. by John Wiley & Sons.

Includes bibliographical references (pages 737-746) and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

0824754018

OCLC:

54505319