Books for Real Analysis and Measure Theory for the IIT JAM Mathematics Exam

1. "Principles of Mathematical Analysis" by Walter Rudin
- This book is a classic and widely used as a textbook for real analysis. It covers the fundamental topics in real analysis including sequences, limits, continuity, differentiation, and integration.
- It provides clear explanations, rigorous proofs, and plenty of exercises to practice. The book is known for its concise and elegant presentation of the material.
- This book is highly recommended for those who want a solid foundation in real analysis.

2. "Real Analysis: Modern Techniques and Their Applications" by Gerald B. Folland
- This book is suitable for those who want a more modern approach to real analysis. It covers the core topics in real analysis such as sequences, limits, continuity, differentiation, integration, and series.
- The book places emphasis on the application of real analysis in other areas of mathematics and provides numerous examples and exercises to reinforce the concepts.
- It also includes additional topics such as Fourier analysis, Lebesgue integration, and metric spaces, which are important for advanced study in analysis.

3. "Measure Theory and Integration" by Michael E. Taylor
- This book is specifically focused on measure theory and integration, which are important topics in real analysis. It provides a rigorous and detailed treatment of measure theory, Lebesgue integration, and related concepts.
- The book starts with the basics of measure theory, including sigma-algebras, measures, and measurable functions. It then moves on to Lebesgue integration, convergence theorems, and differentiation.
- The book also covers topics like product measures, signed measures, and Radon-Nikodym theorem. It includes numerous examples and exercises to strengthen the understanding of the material.

4. "Introduction to Real Analysis" by Bartle and Sherbert
- This book is suitable for beginners in real analysis. It covers the fundamental topics such as sequences, limits, continuity, differentiation, and integration.
- The book provides clear explanations, detailed proofs, and plenty of exercises with varying levels of difficulty. It also includes historical notes to provide a broader perspective on the subject.
- This book is a good choice for self-study or as a supplement to a course on real analysis.

5. "Real Analysis and Applications: Theory in Practice" by Kenneth R. Davidson and Allan P. Donsig
- This book combines theory and applications of real analysis. It covers the core topics in real analysis, including sequences, limits, continuity, differentiation, and integration.
- The book includes numerous examples and applications to areas such as optimization, probability, and differential equations. It also provides exercises to reinforce the concepts and develop problem-solving skills.
- This book is suitable for those who want to see the practical applications of real analysis in other areas of mathematics and related disciplines.

These books provide a comprehensive coverage of the core topics in real analysis and measure theory for the IIT JAM Mathematics Exam. They are highly recommended for building a strong foundation in these subjects and for practicing problem-solving skills.