Syllabus Application
Analysis I
MATH 501
Faculty:
Faculty of Engineering and Natural Sciences
Semester:
Fall 2025-2026
Course:
Analysis I - MATH 501
Classroom:
FENS-L029,FENS-L065
Level of course:
Masters
Course Credits:
SU Credit:3.000, ECTS:10
Prerequisites:
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Corequisites:
-
Course Type:
Lecture
Instructor(s) Information
Gökalp Alpan
- Email: gokalp.alpan@sabanciuniv.edu
Course Information
Catalog Course Description
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.
Course Learning Outcomes:
| 1. | Use Caratheodery definition to construct Lebesgue-Stieltjes measure on the line and Lebesgue measure on any Euclidean space |
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| 2. | Define and use convergence theorems |
| 3. | Define the Lebesgue Integral |
| 4. | Use Radon Nikodym theorem, product measures and Fubini's theorem to evaluate integrals. |
Course Objective
To teach the Measure Theory and Lebesgue Integration, together with some basic aplications to and connections with other parts of Analysis.
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