Hiroshima University Syllabus

Back to syllabus main page
Academic Year School/Graduate School Lecture Code 2024Year School of Science HB100000 Specialized Education 解析学Ａ カイセキガクA Analysis A INOUE AKIHIKO イノウエ　アキヒコ Higashi-Hiroshima 3rd-Year,  First Semester,  2Term (2T) Tues7-8,Thur1-2：Online Lecture Lectures by Teams and ipad. Face-to-face examination. 2.0 J : Japanese 3 : Undergraduate High-Intermediate 25 : Science and Technology 01 : Mathematics/Statistics measure, sigma-additivity, measurable function, integration, monotone convergence theorem, dominated convergence theorem, Lebesgue measure, product measure, Fubini's theorem 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). "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. lesson1 Lebesgue's idealesson2 Integration of simple functionslesson3 Integration of measurable functionslesson4 Monotone convergence theoremlesson5 Dominated convergence theoremlesson6 Sets of measure 0lesson7 1-dimensional integration and primitive functionlesson8 1-dimensional integration by parts and change of variablelesson9 1-dimensional integration -- explicit exampleslesson10 Existence of 1-dimensional Lebesgue measurelesson11 Uniqueness of extension and its applicationlesson12 2-dimensional Lebesgue measurelesson13 Dynkin class theoremlesson14 Fubini's theorem and applicationlesson15 Fubini's theorem and application--continued The PDF of the notes will be distributed through Teams. The PDF of the notes 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. Students are supposed to attend Exercises in Analysis A as well Term paper 25%, Examination 75%. 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.
Back to syllabus main page