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School of Engineering
- Group 2
- Group 3
- Group 4
- Group 5
- Group 6
- Metallurgical Engineering
- Organic and Polymeric Materials
- Inorganic Materials
- Chemical Engineering Course
- Chemical Engineering Course(Chemical Engineering)
- Applied Chemistry Course(Chemical Engineering)
- Polymer Chemistry
- Mechanical Engineering and Science
- Mechanical and Intelligent Systems Engineering
- Mechano-Aerospace Engineering
- International Development Engineering
- Control and Systems Engineering
- Industrial and Systems Engineering
- Electrical and Electronic Engineering
- Computer Science
- Civil Engineering
- Architecture and Building Engineering
- Social Engineering
- Common Cource of Engineering
- Group 2
- School of Bioscience and Biotechnology
- Common Course of Undergraduate School
-
Graduate School of Science and Engineering
- Mathematics
- Physics(Particle- Nuclear- and Astro-Physics)
- Physics(Condensed Matter Physics)
- Chemistry
- Earth and Planetary Sciences
- Chemistry and Materials Science
- Metallurgy and Ceramics Science
- Organic and Polymeric Materials
- Applied Chemistry
- Chemical Engineering
- Common Course of Mechanical Engineering
- Mechanical Sciences and Engineering
- Mechanical and Control Engineering
- Mechanical and Aerospace Engineering
- Common Course of Electronic Engineering
- Electrical and Electronic Engineering
- Physical Electronics
- Communications and Integrated Systems
- Communications and Computer Engineering
- Civil Engineering
- Architecture and Building Engineering
- International Development Engineering
- Nuclear Engineering
- Mathematics
- Graduate School of Bioscience and Biotechnology
-
Interdisciplinary Graduate School of Science and Engineering
- Built Environment
- Energy Sciences
- Computational Intelligence and Systems Science
- Electronic Chemistry
- Materials Science and Engineering
- Innovative and Engineered Materials
- Environmental Chemistry and Engineering
- Environmental Science and Technology
- Mechano-Micro Engineering
- Information Processing
- Electronics and Applied Physics
- Built Environment
- Graduate School of Information Science and Engineering
- Graduate School of Decision Science and Technology
- Graduate School of Innovation Management
- Common Course of Graduate School
- Program for Leading Graduate Schools
- Academic unit or major
- Mathematics
- Instructor(s)
- Tonegawa Yoshihiro
- Class Format
- Lecture (ZOOM)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(H102)
- Group
- -
- Course number
- ZUA.C305
- Credits
- 2
- Academic year
- 2020
- Offered quarter
- 1-2Q
- Syllabus updated
- 2020/9/18
- Lecture notes updated
- 2020/4/23
- Language used
- Japanese
- Access Index
-
Lecture
Lecture 1 Overview of measure theory and Lebesgue integration
2020.5.5(Tue.) 3-4Session
Lecture
Lecture 2 Sigma-algebra
2020.5.12(Tue.) 3-4Session
Lecture
Lecture 3 (Countably additive) measure and its basic properties, completeness
2020.5.19(Tue.) 3-4Session
Lecture
Lecture 4 Measurable functions
2020.5.26(Tue.) 3-4Session
Lecture
Lecture 5 Definition of integral and its basic properties
2020.6.2(Tue.) 3-4Session
Lecture
Lecture 6 Convergence theorems (Monotone convergence theorem, Fatou's lemma and dominated convergence theorem ) and examples
2020.6.9(Tue.) 3-4Session
Lecture
Lecture 7 Applications of convergence theorems
2020.6.16(Tue.) 3-4Session
Lecture
Lecture 8 Extension theorem for measures
2020.6.23(Tue.) 3-4Session
Lecture
Lecture 9 Outer measures and construction of measures
2020.6.30(Tue.) 3-4Session
Lecture
Lecture 10 Relation between Riemann integral and Lebesgue integral
2020.7.7(Tue.) 3-4Session
Lecture
Lecture 11 L^p-spaces and its completeness, fundamental functional inequalities
2020.7.14(Tue.) 3-4Session
Lecture
Lecture 12 Product measure and iterated integral
2020.7.21(Tue.) 3-4Session
Lecture
Lecture 13 Fubini theorem and its applications
2020.7.28(Tue.) 3-4Session
Lecture
Lecture 14 Extension of Fubini theorem
2020.8.4(Tue.) 3-4Session
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