Hiroshima University Syllabus

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Academic Year 2024Year School/Graduate School School of Science
Lecture Code HB100000 Subject Classification Specialized Education
Subject Name 解析学A
Subject Name
Subject Name in
Analysis A
イノウエ アキヒコ
Campus Higashi-Hiroshima Semester/Term 3rd-Year,  First Semester,  2Term
Days, Periods, and Classrooms (2T) Tues7-8,Thur1-2:Online
Lesson Style Lecture Lesson Style
(More Details)
Lectures by Teams and ipad. Face-to-face examination.
Credits 2.0 Class Hours/Week   Language of Instruction J : Japanese
Course Level 3 : Undergraduate High-Intermediate
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students
Keywords measure, sigma-additivity, measurable function, integration, monotone convergence theorem, dominated convergence theorem, Lebesgue measure, product measure, Fubini's theorem 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
(Applicable only to targeted subjects for undergraduate students)
(Knowledge and Understanding)
・Understanding on primary theory of modern mathematics established on classical theory.
(Abilities and Skills)
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). 
Class Objectives
/Class Outline
"Measure" is an abstraction of the concept of "quantity" such as length, area, volume, mass, probability, and number. Measure theory and the theory of integration based on it are extremely useful in various mathematical fields such as analysis, probability theory, and statistics, as well as in their applications. In this lecture, we will learn about measure theory and the theory of integration. 
Class Schedule lesson1 Lebesgue's idea
lesson2 Integration of simple functions
lesson3 Integration of measurable functions
lesson4 Monotone convergence theorem
lesson5 Dominated convergence theorem
lesson6 Sets of measure 0
lesson7 1-dimensional integration and primitive function
lesson8 1-dimensional integration by parts and change of variable
lesson9 1-dimensional integration -- explicit examples
lesson10 Existence of 1-dimensional Lebesgue measure
lesson11 Uniqueness of extension and its application
lesson12 2-dimensional Lebesgue measure
lesson13 Dynkin class theorem
lesson14 Fubini's theorem and application
lesson15 Fubini's theorem and application--continued 
The PDF of the notes will be distributed through Teams. 
PC or AV used in
(More Details) The PDF of the notes 
Learning techniques to be incorporated  
Suggestions on
Preparation and
Try to draw figures as much as possible so that you can intuitively understand the discussions. Also, when reviewing, it is effective to reproduce the discussions you have learned in your notes without looking at anything. 
Requirements Students are supposed to attend Exercises in Analysis A as well 
Grading Method Term paper 25%, Examination 75%.
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. 
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