Measure Theory

By Prof. E. K. Narayanan | IISc Bangalore

Learners enrolled: 683

This course covers measure and integration. We start with abstract measures and their integration theory. Next, we construct the Lebesgue measure and follow it with a detailed study of Borel measures on locally compact Hausdorff spaces. Lp spaces and product measures along with Fubini’s theorem is taken up next. We finish with several classical reasul, Radon-Nikodym theorem, Ries representation theorem and Lebesgue differentiation theorem.

INTENDED AUDIENCE : First year MSc students in mathematics

PREREQUISITES : A course in real analysis and topology

INDUSTRY SUPPORT : Nil

Summary

Course Status :	Completed
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Postgraduate
Start Date :	18 Jan 2021
End Date :	09 Apr 2021
Enrollment Ends :	01 Feb 2021
Exam Date :	24 Apr 2021 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1 : Abstract measures and integration (3 lectures)

Week 2 : Abstract measures and integration (3 lectures)

Week 3 : Outer measure on Rn and properties (3 lectures)

Week 4 : Lebesgue measure and integration (3 lectures)

Week 5 : Borel measures on locally compact spaces (3 lectures)

Week 6 : Lp – spaces and properties (3 lectures)

Week 7 : Product measures (2 lectures)

Week 8 : Product measures (2 lectures)

Week 9 : Complex measures and Radon-Nikodym theorem (2 lectures)

Week 10 : Dual of Lp –spaces (2 lectures)

Week 11 : Riesz representation theorem (2 lectures)

Week 12 : Lebesgue differentiation theorem and absolutely continuous functions (2 lectures)

Books and references

1) E. M. Stein and R. Shakarchi : Real Analysis (Princeton lectures in Analysis)

2) W. Rudin: Real and Complex analysis (McGraw Hill)

3) H. L. Royden: Real analysis (Prentice-Hall)

4) G. B. Folland: Real analysis (Wiley)

5) Robert Ash: Measure Integration and Functional analysis (Academic Press)

Instructor bio

Prof. E. K. Narayanan

IISc Bangalore

I am a professor at the Department of Mathematics, Indian Institute of Science, Bangalore. My primary research area is harmonic analysis.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 24 April 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IISc Bangalore.It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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