Buy An Introduction to Measure and Integration (Graduate Studies in Mathematics) on ✓ FREE SHIPPING on qualified Inder K. Rana ( Author). Measure and Integration: Concepts, Examples and Exercises. INDER K. RANA. Indian Institute of Technology Bombay. India. Department of Mathematics, Indian . Integration is one of the two cornerstones of analysis. Since the fundamental work of Lebesgue, integration has been interpreted in terms of.

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The aim of this course is to give an introduction to the theory of measure ans integration with respect to a measure. The material covered lays foundations for courses in “Functional Analysis”, “Harmonic Analysis” and “Probability Theory”.

Measure and Integration (Prof. Inder K Rana, IIT Bombay) | Mathematics | Audio/video Courses

Starting with the need to define Lebesgue Integral, extension theory for measures will be covered. Abstract theory of integration with respect to a measure and introduction to Lp spaces, product measure spaces, Fubini’s theorem, absolute continuity and Radon-Nikodym theorem will be covered. Measure and Integration Measure and Integration. This is an advanced-level course in Real Analysis.


Lecture 01 – Introduction, Extended Real Numbers. Lecture 03 – Sigma Algebra Generated by a Class.

Lecture 06 – The Length Function and its Properties. Lecture 08 – Uniqueness Problem for Measure.

Lecture 09 – Extension of Measure. Lecture 10 – Outer Measure and its Properties. Lecture 12 – Lebesgue Measure and its Properties.

An Introduction to Measure and Integration

Lecture 13 – Characterization of Lebesgue Measurable Sets. Lecture 14 – Measurable Functions. Lecture 15 – Properties of Measurable Functions.

Lecture 16 – Measurable Functions on Measure Spaces. Lecture 21 – Dominated Convergence Theorem and Applications. Lecture 22 – Lebesgue Integral and innder Properties. Lecture 23 – Denseness of Continuous Function. Lecture 24 – Product Measures: Lecture 25 – Construction of Product Measure.

Lecture 26 – Computation of Product Measure I. Lecture 28 – Integration on Product Spaces. Lecture 30 – Lebesgue Measure and Integral on R2. Lecture 32 – Lebesgue Integral on R2. Lecture 33 – Integrating Complex-Valued Functions. Lecture 38 – Absolutely Continuous Measures. Lecture 39 – Modes of Convergence. Lecture 40 – Convergence in Measure. Measure and Integration Instructor:

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