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.
Analysis I (MATH 501)
2022 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10
Nihat Gökhan Göğüş nggogus@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture
Learner centered,Discussion based learning,Task based learning
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CONTENT
OBJECTIVE
To teach the Measure Theory and Lebesgue Integration, together with some basic aplications to and connections with other parts of Analysis.
LEARNING OUTCOMES
- 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.
Update Date:
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. |