HB110000 Exercises in Analysis A

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Science

Lecture Code HB110000 Subject Classification Specialized Education

Subject Name 解析学Ａ演習

Subject Name
（Katakana）カイセキガクAエンシュウ

Subject Name in
English Exercises in Analysis A

Instructor NAGOJI HIROTATSU,DAY JASON JUNICHI

Instructor
(Katakana) ナゴジ　ヒロタツ,デイ　ジェイソン　ジュンイチ

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

Days, Periods, and Classrooms (2T) Weds1-2,Thur5-6：SCI E210

Lesson Style Seminar 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 Mathmatics 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
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
・To acquire skills to formulate and solve mathematical questions.

Class Objectives
/Class Outline You will deepen your understanding of what you have learned in Analysis A by solving problems given by your instructor and by submitting answers to assigned assignments.

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 Lebesgue measure
14. Change of variables
15. Application

Text/Reference
Books,etc. No textbooks will be used.

PC or AV used in
Class,etc. moodle

(More Details)

Learning techniques to be incorporated Post-class Report

Suggestions on
Preparation and
Review To understand math, it is important to first try to solve problems yourself. If you don't understand a problem right away, wait a while and try again.

Requirements Students are supposed to attend Analysis A as well

Grading Method Reports

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

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	HB110000	Subject Classification	Specialized Education
Subject Name	解析学Ａ演習
Subject Name （Katakana）	カイセキガクAエンシュウ
Subject Name in English	Exercises in Analysis A
Instructor	NAGOJI HIROTATSU,DAY JASON JUNICHI
Instructor (Katakana)	ナゴジ　ヒロタツ,デイ　ジェイソン　ジュンイチ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Weds1-2,Thur5-6：SCI E210
Lesson Style	Seminar	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	Mathmatics 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 （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). ・To acquire skills to formulate and solve mathematical questions.
Class Objectives /Class Outline	You will deepen your understanding of what you have learned in Analysis A by solving problems given by your instructor and by submitting answers to assigned assignments.
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 Lebesgue measure 14. Change of variables 15. Application
Text/Reference Books,etc.	No textbooks will be used.
PC or AV used in Class,etc.	moodle
(More Details)
Learning techniques to be incorporated	Post-class Report
Suggestions on Preparation and Review	To understand math, it is important to first try to solve problems yourself. If you don't understand a problem right away, wait a while and try again.
Requirements	Students are supposed to attend Analysis A as well
Grading Method	Reports
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
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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