Measure and Integration

1. Front Matter

   Pages i-xii

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2. Preliminaries

   • Satish Shirali, Harkrishan Lal Vasudeva

   Pages 1-42

3. Measure in Euclidean Space

   • Satish Shirali, Harkrishan Lal Vasudeva

   Pages 43-108

4. Measure Spaces and Integration

   • Satish Shirali, Harkrishan Lal Vasudeva

   Pages 109-162

5. Fourier Series

   • Satish Shirali, Harkrishan Lal Vasudeva

   Pages 163-209

6. Differentiation

   • Satish Shirali, Harkrishan Lal Vasudeva

   Pages 211-336

7. Lebesgue Spaces and Modes of Convergence

   • Satish Shirali, Harkrishan Lal Vasudeva

   Pages 337-374

8. Product Measure and Completion

   • Satish Shirali, Harkrishan Lal Vasudeva

   Pages 375-404

9. Hints

   • Satish Shirali, Harkrishan Lal Vasudeva

   Pages 405-590

10. Back Matter

    Pages 591-598

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This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis.


Proceeding at a leisurely, student-friendly pace, the authors begin by recalling elementary notions of real analysis before proceeding to measure theory and Lebesgue integration. Further chapters cover Fourier series, differentiation, modes of convergence, and product measures. Noteworthy topics discussed in the text include L^p spaces, the Radon–Nikodým Theorem, signed measures, the Riesz Representation Theorem, and the Tonelli and Fubini Theorems.


This textbook, based on extensive teaching experience, is written for senior undergraduate and beginning graduate students in mathematics. With each topic carefully motivated and hints to more than 300 exercises, it is the ideal companion for self-study or use alongside lecture courses.

• Measure theory
• Integration theory
• Lebesgue measure
• Fourier series
• Fubini theorem
• Tonelli theorem
• Lp spaces
• Vitali covering theorem
• Radon-Nikodym theorem
• Product measure
• Cantor set
• Bounded variation
• Absolute continuity

• Formerly of Panjab University, Chandigarh, India

  Satish Shirali, Harkrishan Lal Vasudeva

​Satish Shirali's research interest are in Banach *algebras, elliptic boundary value problems, fuzzy measures, and Harkrishan Vasudeva's interests are in functional analysis. This is their fourth joint textbook, having previous published An Introduction to Mathematical Analysis (2014), Multivariable Analysis (2011) and Metric Spaces (2006). Shirali is also the author of the book A Concise Introduction to Measure Theory (2018), and Vasudeva is the author of Elements of Hilbert Spaces and Operator Theory (2017) and co-author of An Introduction to Complex Analysis (2005).

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