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Website for M301: Lebesgue Integration,

Spring 2026

This the website for the course M301:Lebesgue Integration. I will be maintaining this website regularly during the course; please visit it regulalry.

This is a course in Measure Theory. It is undoubtedly one of the most abstract and difficult topics that a mathematics student encounetrs. It is also one of the most fundamental topics that a serious mathematics student needs to master. Without a solid understanding of Measure Theory, a large number of extremely important and interesting topics will be completely inaccessible. These topics include (but are not limited to) Functional Analysis, Partial Differential Equations, Probability Theory, Harmonic Analysis, Operator Theory, Dynamical Systems, Ergodic Theory and Geometric Measure Theory.

Hence, while this course is extremely difficult and challenging, it is at the end also very rewarding. If you are registered for this course, you have to put in a lot of effort to do well.

We will be using the following references

1) ``Measure and Integration'' by S. Kesavan. This is the main book we will be following.

I recommend that you purchase this book.

Other books that we might consult from time to time are

2) ``Real Analysis: Modern Techniques and Their Applications'' by G. Folland.

3) ``Real Analysis'' by E. Stein and R. Shakarchi.

4) ``Real and Complex Analysis'' by W. Rudin.

5) ``Fourier Analysis'' by E.Stein and R.Shakarchi.

Grading: Continuous Assesment (Homework + Quizzes) = 30%

Mid Term = 30%

Final Exam = 40%

Grading will be absolute.

Attendance is compulsory. I will deduct two points from the Continuous Assement portion for every single class that you miss without a valid reason. Hence, even missing one class can affect your grade (for example, if your final score was otherwise 91, but you missed one class, you will end up getting an AB instead of an AA).

Attendance will be taken 10 minutes after the class starts. If you enter the class after 10 minutes, you will be marked absent.

Examples of valid reasons include: being unwell accompanied with a doctor's note, an important exam that you might have to give (such as CSIR etc) that clashes with the timing of the course or a family emergency. These reasons have to be accompanied by a valid proof (for example, if you are claiming that you missed a class due to an exam, you will need to show me your admit card for the exam). Examples of reasons that are not valid include: caliming that you are unwell without any doctor's note, saying that you woke up late etc. If you have a valid reason to miss a class, I will not deduct the two points. Howvever, you are still responsilbe for studying the topics that you missed.

If your attendance is below 80 percent, you will not be allowed to sit for the final exam. I will however, mark everyone present for the FIRST week of classes (5th to 9th January, 2026). You are nevertheless responsible for all the material covered in the first week.

Clarification: The continuous assessment portion will be computed as follows.

Let T1 be the sum total of the scores you get in the HW and quizzes. Let

E1 be the marks I award you for attending the extra classes I take (how much is

E1 will be decided by me later on). Let N be the number of (regular) classes you miss

without a valid reason. Let T2:= Min(30, T1+E1). Let T3 = T2-2*N. Finally

let T4:= Max(T3, 0). Your continuous assesment score is T4.

Reading Assignments (for your own benefit)

Suggested Reading 1

Homework Assignments

The first homework is due in class on 16th Jan (Fri) by 10:25 am.

Nothing will be accepted after 10:25 am.

Quizzes

I will take a quiz on 16th Jan (Fri) in class. Your answer script has to be submitted by 10:25 am. Nothing will be accepted after 10:25 am.

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