Michael E. Taylor, University of North Carolina, Chapel Hill, NC.

• ChaptersChapter 1. The Riemann integralChapter 2. Lebesgue measure on the lineChapter 3. Integration on measure spacesChapter 4. $L^p$ spacesChapter 5. The Caratheodory construction of measuresChapter 6. Product measuresChapter 7. Lebesgue measure on $\mathbb {R}^n$ and on manifoldsChapter 8. Signed measures and complex measuresChapter 9. $L^p$ spaces, IIChapter 10. Sobolev spacesChapter 11. Maximal functions and a.e. phenomenaChapter 12. Hausdorff's $r$-dimensional measuresChapter 13. Radon measuresChapter 14. Ergodic theoryChapter 15. Probability spaces and random variablesChapter 16. Wiener measure and Brownian motionChapter 17. Conditional expectation and martingalesAppendix A. Metric spaces, topological spaces, and compactnessAppendix B. Derivatives, diffeomorphisms, and manifoldsAppendix C. The Whitney Extension TheoremAppendix D. The Marcinkiewicz Interpolation TheoremAppendix E. Sard's TheoremAppendix F. A change of variable theorem for many-to-one mapsAppendix G. Integration of differential formsAppendix H. Change of variables revisitedAppendix I. The Gauss-Green formula on Lipschitz domains

Taylor's treatment throughout is elegant and very efficient ... I found reading the text very enjoyable."" —MAA Reviews""The book is very understandable, requiring only a basic knowledge of analysis. It can be warmly recommended to a broad spectrum of readers, to graduate students as well as young researchers."" —EMS Newsletter""This monograph provides a quite comprehensive presentation of measure and integration theory and of some of their applications."" —Mathematical Reviews

Michael E. Taylor, University of North Carolina, Chapel Hill, NC.

• ChaptersChapter 1. The Riemann integralChapter 2. Lebesgue measure on the lineChapter 3. Integration on measure spacesChapter 4. $L^p$ spacesChapter 5. The Caratheodory construction of measuresChapter 6. Product measuresChapter 7. Lebesgue measure on $\mathbb {R}^n$ and on manifoldsChapter 8. Signed measures and complex measuresChapter 9. $L^p$ spaces, IIChapter 10. Sobolev spacesChapter 11. Maximal functions and a.e. phenomenaChapter 12. Hausdorff's $r$-dimensional measuresChapter 13. Radon measuresChapter 14. Ergodic theoryChapter 15. Probability spaces and random variablesChapter 16. Wiener measure and Brownian motionChapter 17. Conditional expectation and martingalesAppendix A. Metric spaces, topological spaces, and compactnessAppendix B. Derivatives, diffeomorphisms, and manifoldsAppendix C. The Whitney Extension TheoremAppendix D. The Marcinkiewicz Interpolation TheoremAppendix E. Sard's TheoremAppendix F. A change of variable theorem for many-to-one mapsAppendix G. Integration of differential formsAppendix H. Change of variables revisitedAppendix I. The Gauss-Green formula on Lipschitz domains

Taylor's treatment throughout is elegant and very efficient ... I found reading the text very enjoyable."" —MAA Reviews""The book is very understandable, requiring only a basic knowledge of analysis. It can be warmly recommended to a broad spectrum of readers, to graduate students as well as young researchers."" —EMS Newsletter""This monograph provides a quite comprehensive presentation of measure and integration theory and of some of their applications."" —Mathematical Reviews

Michael E. Taylor, University of North Carolina, Chapel Hill, NC.

• ChaptersChapter 1. The Riemann integralChapter 2. Lebesgue measure on the lineChapter 3. Integration on measure spacesChapter 4. $L^p$ spacesChapter 5. The Caratheodory construction of measuresChapter 6. Product measuresChapter 7. Lebesgue measure on $\mathbb {R}^n$ and on manifoldsChapter 8. Signed measures and complex measuresChapter 9. $L^p$ spaces, IIChapter 10. Sobolev spacesChapter 11. Maximal functions and a.e. phenomenaChapter 12. Hausdorff's $r$-dimensional measuresChapter 13. Radon measuresChapter 14. Ergodic theoryChapter 15. Probability spaces and random variablesChapter 16. Wiener measure and Brownian motionChapter 17. Conditional expectation and martingalesAppendix A. Metric spaces, topological spaces, and compactnessAppendix B. Derivatives, diffeomorphisms, and manifoldsAppendix C. The Whitney Extension TheoremAppendix D. The Marcinkiewicz Interpolation TheoremAppendix E. Sard's TheoremAppendix F. A change of variable theorem for many-to-one mapsAppendix G. Integration of differential formsAppendix H. Change of variables revisitedAppendix I. The Gauss-Green formula on Lipschitz domains

Taylor's treatment throughout is elegant and very efficient ... I found reading the text very enjoyable."" —MAA Reviews""The book is very understandable, requiring only a basic knowledge of analysis. It can be warmly recommended to a broad spectrum of readers, to graduate students as well as young researchers."" —EMS Newsletter""This monograph provides a quite comprehensive presentation of measure and integration theory and of some of their applications."" —Mathematical Reviews