Analysis I (MATH 501)

2021 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10.00
Turgay Bayraktar tbayraktar@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture
Learner centered,Discussion based learning,Task based learning
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CONTENT

Lebesgue measure and integration on the line. Convergence theorems. General measure and integration. Lp spaces. Decomposition of measures. Radon Nikodym theorem. Product measures and Fubini's theorem.

OBJECTIVE

To teach the Measure Theory and Lebesgue Integration, together with some basic aplications to and connections with other parts of Analysis.

LEARNING OUTCOME

Use Caratheodery definition to construct Lebesgue-Stieltjes measure on the line and Lebesgue measure on any Euclidean space
Define and use convergence theorems
Define the Lebesgue Integral
Use Radon Nikodym theorem, product measures and Fubini's theorem to evaluate integrals.

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Midterm 30
Homework 60
Other 10

RECOMENDED or REQUIRED READINGS

Readings

Walter Rudin, Real and Complex Analysis, McGraw-Hill, London, New York.