Measure Theory
Explore all the details of measurement theory with the Measure Theory certification course from IIT Bombay.
Online
12 WeeksQuick 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
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)
The certification course is an online programme that provides students with an understanding of measurements in mathematics.
Yes, students will receive a certification upon successful completion of the course, however, they have to pass the qualifying examination for the certification.
Students for the certification course typically have access to course materials such as lecture notes, textbooks, problem sets and more.
The online programme is a 12-week certification programme with a hands-on learning approach and flexible learning options.
Students must visit the official course page and complete the enrollment process by providing details on the website and paying the course fees.