Hiroshima University Syllabus |

Japanese

Academic Year 2024Year 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

EnglishAnalysis A Instructor INOUE AKIHIKO Instructor

(Katakana)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

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 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--continuedText/Reference

Books,etc.The PDF of the notes will be distributed through Teams. PC or AV used in

Class,etc.(More Details) The PDF of the notes Learning techniques to be incorporated Suggestions on

Preparation and

ReviewTry 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 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.