Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study, Virtual Classroom	Video and Text Based

Course Overview

The measure Theory Certification course is a 12-week online programme that offers a comprehensive exploration into the fundamental concepts and applications of measure theory. Students will gain a deep understanding of the theoretical foundations of measure theory and its practical significance in mathematical physics with the Measure Theory Certification by NPTEL.

The measure Theory training will develop the analytical skills necessary to tackle advanced mathematical problems and applications. Students are equipped with a solid foundation in measure theory, empowering them to engage with complex mathematical concepts. They are at the same time provided with a versatile toolkit for solving real-world problems.

Also Read: Online Mathematics Certification Courses

The Highlights

IIT Bombay recognised Completion Certificate
Learning from Trained Faculty Members
Free Course Readings
Hands-on projects

Programme Offerings

online learning
Robust curriculum
Hands-on Learning
Certified faculty and mentors

Courses and Certificate Fees

Certificate Availability	Certificate Providing Authority
yes	IIT Bombay

Eligibility Criteria

Academic Qualifications

Candidates for the Measure Theory training are required to have a B.Tech Dual degree in Electrical, M.Sc. Physics, for the programme.

Certification Qualifying Details

Candidates for the Measure Theory certification course must qualify for the final examination to receive the completion certificate.

What you will learn

After completing the Measure Theory Certification syllabus, students are provided with a comprehensive understanding of advanced mathematical concepts and techniques essential in various fields. The online course provides a solid foundation in measure theory and the analytical skills necessary to excel in a variety of mathematical disciplines and professional settings.

Who it is for

StatisticianData ScientistMathematician

The Measure Theory training is ideal for undergraduate or graduate students studying mathematics or related disciplines.

The course is apt for the following professionals:

Admission Details

To join the Measure Theory classes, candidates must follow the below-mentioned steps:

Step 1: Visit the official course URL:

https://nptel.ac.in/courses/111101100

Step 2: Log in to the website and enrol for the programme.

Step 3: Enter relevant academic and personal details.

Step 4: Pay the course fee to complete the enrollment process

Step 5: Start learning

Application Details

Candidates need to visit the official course page to enrol in the online Measure Theory Certification Course. After that, they need to complete the enrollment process by entering their details and course fees.

The Syllabus

Lecture 1A: Introduction, Extended Real Numbers

Lecture 1B: Introduction, Extended Real Numbers

Lecture 2A: Algebra and Sigma Algebra of Subsets of a Set

Lecture 2B: Algebra and Sigma Algebra of Subsets of a Set

Lecture 3A: Sigma Algebra generated by a Class

Lecture 3B: Sigma Algebra generated by a Class

Lecture 4A: Monotone Class

Lecture 4B: Monotone Class

Lecture 5A: Set Functions

Lecture 5B: Set Functions

Lecture 6A: The Length Function and its Properties

Lecture 6B: The Length Function and its Properties

Lecture 7A: Countably Additive Set Functions on Intervals

Lecture 7B: Countably Additive Set Functions on Intervals

Lecture 8A: Uniqueness Problem for Measure

Lecture 8B: Uniqueness Problem for Measure

Lecture 9A: Extension of Measure

Lecture 9B: Extension of Measure

Lecture 10A: Outer Measure and its Properties

Lecture 10B: Outer Measure and its Properties

Lecture 11A: Measurable Sets

Lecture 11B: Measurable Sets

Lecture 12A: Lebesgue Measure and its Properties

Lecture 12B: Lebesgue Measure and its Properties

Lecture 13A: Characterization of Lebesgue Measurable Sets

Lecture 13B: Characterization of Lebesgue Measurable Sets

Lecture 14A: Measurable Functions

Lecture 14B: Measurable Functions

Lecture 15A: Properties of Measurable Functions

Lecture 15B: Properties of Measurable Functions

Lecture 16A: Measurable Functions on Measure Spaces

Lecture 16B: Measurable Functions on Measure Spaces

Lecture 17A: Integral of Nonnegative Simple Measurable Functions

Lecture 17B: Integral of Nonnegative Simple Measurable Functions

Lecture 18A: Properties of Nonnegative Simple Measurable Functions

Lecture 18B: Properties of Nonnegative Simple Measurable Functions

Lecture 19A: Monotone Convergence Theorem and Fatou's Lemma

Lecture 19B: Monotone Convergence Theorem and Fatou's Lemma

Lecture 20A: Properties of Integrable Functions and Dominated Convergence Theorem

Lecture 20B: Properties of Integrable Functions and Dominated Convergence Theorem

Lecture 21A: Dominated Convergence Theorem and Applications

Lecture 21B: Dominated Convergence Theorem and Applications

Lecture 22A: Lebesgue Integral and its Properties

Lecture 22B: Lebesgue Integral and its Properties

Lecture 23A: Product Measure, an Introduction

Lecture 23B: Product Measure, an Introduction

Lecture 24A: Construction of Product Measures

Lecture 24B: Construction of Product Measures

Lecture 25A: Computation of Product Measure - I

Lecture 25B: Computation of Product Measure - I

Lecture 26A: Computation of Product Measure - II

Lecture 26B: Computation of Product Measure - II

Lecture 27A: Integration on Product Spaces

Lecture 27B: Integration on Product Spaces

Lecture 28A: Fubini's Theorems

Lecture 28B: Fubini's Theorems

Lecture 29A: Lebesgue Measure and Integral on R2

Lecture 29B: Lebesgue Measure and Integral on R2

Lecture 30A: Properties of Lebesgue Measure on R2

Lecture 30B: Properties of Lebesgue Measure on R2

Lecture 31A: Lebesgue Integral on R2

Lecture 31B: Lebesgue Integral on R2

Evaluation process

Candidates for the Measure Theory certification course are required to appear for the examinations to receive the completion certificate.

IIT Bombay Frequently Asked Questions (FAQ's)

1: Can the Measure Theory certification course be pursued online?

The certification course is an online programme that provides students with an understanding of measurements in mathematics.

2: Is there any certification offered upon completion of the Measure Theory online course?

Yes, students will receive a certification upon successful completion of the course, however, they have to pass the qualifying examination for the certification.

3: What resources are provided to support students during the Measure Theory training?

Students for the certification course typically have access to course materials such as lecture notes, textbooks, problem sets and more.

4: What is the duration of the Measure Theory certification course?

The online programme is a 12-week certification programme with a hands-on learning approach and flexible learning options.

5: How can I enrol in the Measure Theory training?

Students must visit the official course page and complete the enrollment process by providing details on the website and paying the course fees.