HB100000 Analysis A

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Science

Lecture Code HB100000 Subject Classification Specialized Education

Subject Name 解析学Ａ

Subject Name
（Katakana）カイセキガクA

Subject Name in
English Analysis A

Instructor OKAMOTO MAMORU

Instructor
(Katakana) オカモト　マモル

Campus Higashi-Hiroshima Semester/Term 3rd-Year, First Semester, 2Term

Days, Periods, and Classrooms (2T) Tues1-2,Thur3-4：SCI E209

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

Lectures using blackboards

Credits 2.0 Class Hours/Week 4 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
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Mathematics
（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 1. Measurable spaces
2. Measurable functions
3. Measure spaces
4. Monotone convergence theorem
5. Dominated convergence theorem
6. Completion
7. Outer measures
8. Extension theorem
9. Lebesgue measure
10. Product measurable spaces
11. Product measure spaces
12. Fubini's theorem
13. Properties of the Lebesgue measure
14. Change of variables
15. Application

Text/Reference
Books,etc. 伊藤清三：ルベーグ積分入門（新装版）、裳華房
G. B. Folland: Real Analysis, Wiley, 2nd edition

PC or AV used in
Class,etc. moodle

(More Details)

Learning techniques to be incorporated

Suggestions on
Preparation and
Review For each lesson, make sure you can state definitions, notation, and theorem statements accurately, and that you can explain the flow and main ideas of theorem proofs.

Requirements Students are supposed to attend Exercises in Analysis A as well.

Grading Method Examination

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message Make sure to do thorough preparation and review.

Other

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.

Academic Year	2026Year	School/Graduate School	School of Science
Lecture Code	HB100000	Subject Classification	Specialized Education
Subject Name	解析学Ａ
Subject Name （Katakana）	カイセキガクA
Subject Name in English	Analysis A
Instructor	OKAMOTO MAMORU
Instructor (Katakana)	オカモト　マモル
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Tues1-2,Thur3-4：SCI E209
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face
Lectures using blackboards
Credits	2.0	Class Hours/Week	4	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 Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Mathematics （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	1. Measurable spaces 2. Measurable functions 3. Measure spaces 4. Monotone convergence theorem 5. Dominated convergence theorem 6. Completion 7. Outer measures 8. Extension theorem 9. Lebesgue measure 10. Product measurable spaces 11. Product measure spaces 12. Fubini's theorem 13. Properties of the Lebesgue measure 14. Change of variables 15. Application
Text/Reference Books,etc.	伊藤清三：ルベーグ積分入門（新装版）、裳華房 G. B. Folland: Real Analysis, Wiley, 2nd edition
PC or AV used in Class,etc.	moodle
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	For each lesson, make sure you can state definitions, notation, and theorem statements accurately, and that you can explain the flow and main ideas of theorem proofs.
Requirements	Students are supposed to attend Exercises in Analysis A as well.
Grading Method	Examination
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	Make sure to do thorough preparation and review.
Other
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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