Measure Theory
Explore all the details of measurement theory with the Measure Theory certification course from IIT Bombay.
Online
12 Weeks
Free 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
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
- Extended Real Numbers Lecture 1B Introduction, Extended Real Numbers
- Algebra and Sigma Algebra of Subsets of a Set
- Algebra and Sigma Algebra of Subsets of a Set
- Sigma Algebra generated by a Class
- Sigma Algebra generated by a Class
- Countably Additive Set Functions on Intervals
- Countably Additive Set Functions on Intervals Uniqueness Problem for Measure
- Uniqueness Problem for Measure
- Extension of Measure
- Extension of Measure
- Outer Measure and its Properties
- Outer Measure and its Properties
- Measurable Sets
- Measurable Sets
- Lebesgue Measure and its Properties
- Lebesgue Measure and its Properties
- Characterization of Lebesgue Measurable Sets
- Characterization of Lebesgue Measurable Sets
- Measurable FunctionsMeasurable Functions
- Properties of Measurable Functions Properties of Measurable Functions
- Measurable Functions on Measure Spaces
- Measurable Functions on Measure Spaces
- Integral of Nonnegative Simple Measurable Functions
- Integral of Nonnegative Simple Measurable FunctionsProperties of Nonnegative Simple Measurable FunctionsProperties of Nonnegative Simple Measurable Functions Monotone Convergence Theorem and Fatou's Lemma
- Monotone Convergence Theorem and Fatou's Lemma
- Properties of Integrable Functions and Dominated Convergence Theorem
- Properties of Integrable Functions and Dominated Convergence Theorem
- Dominated Convergence Theorem and Applications
- Dominated Convergence Theorem and Applications
- Lebesgue Integral and its Properties
- Lebesgue Integral and its Properties Product Measure, an Introduction Product
- Measure, an Introduction Construction of Product Measures
- Construction of Product Measures
- Computation of Product Measure - I
- Computation of Product Measure - I
- Computation of Product Measure - II
- Computation of Product Measure - II
- Integration on Product Spaces
- Integration on Product Spaces
- Fubini's Theorems Fubini's Theorems
- Lebesgue Measure and Integral on R2
- Lebesgue Measure and Integral on R2
- Properties of Lebesgue Measure on R2
- Properties of Lebesgue Measure on R2
- Lebesgue Integral on R2
- 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.