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Taylor, Michael E., 1946-

Measure theory and integration / Michael E. Taylor. - xiii, 319 pages : illustrations ; 27 cm. - Graduate studies in mathematics, v. 76 1065-7339 ; . - Graduate studies in mathematics, volume 76. .

Includes bibliographical references (pages 311-313) and indexes.

Table Of Contents: Introduction The Riemann Integral Lebesgue Measure on the Line Integration on Measure Spaces Lp Spaces The Caratheodory Construction of Measures Product Measures Lebesgue Measure on Rn and on Manifolds Signed Measures and Complex Measures Lp Spaces, II Sobolev Spaces Maximal Functions and A.E. Phenomena Hausdorff's r-Dimensional Measures Radon Measures Ergodic Theory Probability Spaces and Random Variables Wiener Measure and Brownian Motion Conditional Expectation and Martingales Appendix A. Metric Spaces, Topological Spaces, and Compactness Appendix B. Derivatives, Diffeomorphisms, and Manifolds Appendix C. The Whitney Extension Theorem Appendix D. The Marcinkiewicz Interpolation Theorem Appendix E. Sard's Theorem Appendix F. A Change of Variable Theorem for Many-to-one Maps Appendix G. Integration of Differential Forms Appendix H. Change of Variables Revisited Appendix I. The Gauss-Green Formula on Lipschitz Domains Bibliography Symbol Index Subject Index

ISBN: 9780821841808

Subjects--Topical Terms:
Measure theory.
Riemann integral.
Convergence.
Probabilities.

LC Class. No.: QA312 / .T387 2006

Dewey Class. No.: