math202 measure and integration

MATH202 Measure and Integration

Classes begin on January 2, 2014. Students are expected to have a copy of the text book by Gar de Barra. The Indian print by New Age International can be found here and it costs Rs 199 (and I am not very happy with typesetting though the original edition is nicely typeset.) You can have H L Royden's book with you and it is very nice. Baby Rudin has some material that we will cover and Papa Rudin has much more!

You should revise the basic real analysis especially the construction and properties of Cantor's set. A knowledge of Riemann integral will be helpful.

Lecture timings: Monday - Friday 9:40-10:35 at LR-I

Syllabus: Lebesgue outer measure, measurable sets, regularity, measurable functions, Borel and Lebesgue

measurability, non-measurable sets.

Integration of non-negative functions, the general integral, integration of series, Riemann and Lebesgue integrals.

Functions of bounded variation, Lebesgue differentiation theorem, differentiation and integration, absolute continuity of functions.

Measures and outer measures, measure spaces, integration with respect to a measure.

The L^p spaces Hölder and Minkowski inequalities , completeness of L^p spaces, convergence in measure, almost uniform convergence, Egorov's theorem

Textbook:

• G. De Barra, Measure Theory and Integration, Wiley Eastern, 1981

References:

• Edwin Hewitt, Karl Stromberg, Real and Abstract Analysis, GTM 25, Springer, Berlin, 1988.

• H. L. Royden, Real Analysis, Pearson, 2008.

Internal Assessment:

Internal assessment marks will be based on common in-house examination (20 marks) as well as a class test (10 marks) on Feb 3, 2014.