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
10.00
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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| Programs\Type | Required | Core Elective | Area Elective |
| MA-European Studies | |||
| MA-European Studies-Non Thesis | |||
| MA-Political Science | |||
| MA-Political Science-Non Thes | |||
| MA-Visual Arts&Vis. Com Des-NT | |||
| MA-Visual Arts&Visual Com Des | |||
| MS-Bio. Sci. & Bioeng. LFI | |||
| MS-Bio. Sci. & Bioeng. LFI-ENG | |||
| MS-Biological Sci&Bioeng. | * | ||
| MS-Computer Sci.&Eng. LFI | |||
| MS-Computer Sci.&Eng. LFI-ENG | |||
| MS-Computer Science and Eng. | * | ||
| MS-Cyber Security(with thesis) | * | ||
| MS-Data Science | |||
| MS-Elec. Eng&Comp Sc.LFI-ENG | |||
| MS-Electronics Eng&Comp Sc.LFI | |||
| MS-Electronics Eng&Computer Sc | * | ||
| MS-Electronics Eng. | * | ||
| MS-Electronics Eng. LFI | |||
| MS-Electronics Eng. LFI-ENG | |||
| MS-Energy Techno.&Man. | * | ||
| MS-Industrial Eng. LFI-ENG | |||
| MS-Industrial Engineering | * | ||
| MS-Industrial Engineering LFI | |||
| MS-Manufacturing Eng-Non Thes | * | ||
| MS-Manufacturing Engineering | * | ||
| MS-Materials Sci & Engineering | * | ||
| MS-Materials Sci. & Eng. LFI | |||
| MS-Materials Sci.&Eng. LFI-ENG | |||
| MS-Mathematics | * | ||
| MS-Mechatronics | * | ||
| MS-Mechatronics LFI | |||
| MS-Mechatronics LFI-ENG | |||
| MS-Physics | |||
| MS-Physics-Non Thesis | * | ||
| MS-Psychology | |||
| MS-Psychology-Non Thesis | |||
| PHD-Biological Sci&Bioeng. | * | ||
| PHD-Comp. Sci and Eng.after UG | * | ||
| PHD-Computer Science and Eng. | * | ||
| PHD-Cyber Security | * | ||
| PHD-Electronics Eng&ComputerSc | * | ||
| PHD-Electronics Eng. | * | ||
| PHD-Electronics Eng. after UG | * | ||
| PHD-Experimental Psychology | |||
| PHD-Industrial Engineering | * | ||
| PHD-Management | |||
| PHD-Manufacturing Eng after UG | * | ||
| PHD-Manufacturing Engineering | * | ||
| PHD-Materials Sci.&Engineering | * | ||
| PHD-Mathematics | |||
| PHD-Mechatronics | * | ||
| PHD-Mechatronics after UG | * | ||
| PHD-Physics | |||
| PHD-Physics after UG | |||
| PHD-Social Psychology | |||
| PHDBIO after UG | * | ||
| PHDCYSEC after UG | * | ||
| PHDEECS after UG | * | ||
| PHDEPSY after UG | |||
| PHDIE after UG | * | ||
| PHDMAN after UG | |||
| PHDMAN after UG-Finance | |||
| PHDMAN after UG-Man. and Org. | |||
| PHDMAN after UG-Op.&Sup. Cha. | |||
| PHDMAN-Finance Area | |||
| PHDMAN-Man. and Org. Area | |||
| PHDMAN-Op. & Supp. Chain Area | |||
| PHDMAT after UG | * | ||
| PHDMATH after UG | * | ||
| PHDSPSY after UG |
CONTENT
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.
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. |