Lecture Details :
Measure and Integration by Prof. Inder K Rana ,Department of Mathematics, IIT Bombay. For more details on NPTEL visit http://nptel.iitm.ac.in
Course Description :
Need to define Lebesgue Integral,Semi-algebra, Algebra, Monotone class, Sigma-algebra, Monotone class theorem. Measure spaces.Extension of measures from algebras to the generated sigma-algebras: Measurable sets; Lebesgue Measure and its properties.
Measurable functions and their properties; Integration and Convergence theorems, Lebesgue integral, Fundamental Theorem of Calculus for Lebesgue Integrals (an outline)
Product measure spaces, Fubini's theorem
Absolute continuity of measures, Radon-Nikodym theorem Introduction
to Lp spaces, Riesz-Fischer theorem; Riesz Representation theorem for L2 spaces.
Other Resources :
Other Mathematics Courses
- Pre-algebra by Khan Academy
- Stochastic Processes by IIT Delhi
- Linear Algebra - Khan Academy by Khan Academy
- Math 3C: Probability for Math Science by UCLA
- Algebra by Khan Academy
- Linear Algebra by The University of New South Wales
- Advanced Matrix Theory by IISc Bangalore
- Algebra I Worked Examples by Khan Academy
- Miscellaneous Mathematics by Other
- Mathematics for Finance and Actuarial Studies 1 by Other
» check out the complete list of Mathematics Video lectures
Get Your Degree!
Find schools and get information on the program that’s right for you.
Powered by Campus Explorer