ANDHRA UNIVERSITY, WALTAIR

 

M.Sc. APPLIED MATHEMATICS, THIRD SEMSTER

 

AM-301 : MEASURE THEORY

                                    

[A total of seven questions are to be set.  All questions carry equal marks.  The first question which is compulsory carries 20 marks.  It consists of 4 short answer sub questions each of five marks covering the entire syllabus.  The remaining six questions each carrying 20 marks are to be set as suggested in the body of the syllabi.]

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Lebesgue Measure: Introduction, Outer measure, Measurable sets and Lebesgue measure, A non measurable set, measurable functions, Littlewood’s three principles.

The Lebesgue integral: The Riemann integral, The Lebesgue integral of a bounded function over a set of finite measure.  The integral of a non negative function.  The general Lebesgue integral, convergence in measure.  (Chapters 3 and 4 of the Text book)

( Three questions are to be set)

Differentiation and Integration: Differentiation of Monotonic functions, Functions of bounded variation, Differentiation of an integral, Absolute continuity, convex functions.

The classical banach spaces: The LP spaces, The Holder and Minkowski inequalities , convergence and completeness, Bounded linear functionals on the LP spaces ( Chapters 5 and 6 of the Text Book)

( Three questions are to be set)

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Text book:

Real Analysis, H.L.Royden – Macmillan publishing Company.