Μeasure Theory

Course Information
TitleΘΕΩΡΙΑ ΜΕΤΡΟΥ ΚΑΙ ΟΛΟΚΛΗΡΩΣΗΣ / Μeasure Theory
Code0643
FacultySciences
SchoolMathematics
Cycle / Level2nd / Postgraduate
Teaching PeriodWinter
CoordinatorRomanos diogenis Malikiosis
CommonYes
StatusActive
Course ID40000031

Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)

Registered students: 12
OrientationAttendance TypeSemesterYearECTS
THEŌRĪTIKA MATHĪMATIKACore Courses A21110

Class Information
Academic Year2019 – 2020
Class PeriodWinter
Faculty Instructors
Weekly Hours3
Class ID
600148286
Course Category
General Foundation
Mode of Delivery
  • Face to face
Language of Instruction
  • Greek (Instruction, Examination)
Course Content (Syllabus)
σ-algebras. Measures. Borel measures. Measurable and integrable functions. Modes of convergence. Product measure. Fubini's theorem. Lebesgue integral on R^n. Signed measures. Absolutely continuous and singular measures. Hahn decomposition theorem. Jordan decomposition theorem. Lebesgue-Radon-Nikodym theorem. Functions of bounded variation. Basic theory of L^p spaces.
Keywords
Lebesgue measure and integral
Educational Material Types
  • Book
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures391.3
Reading Assigment2598.6
Exams20.1
Total30010
Student Assessment
Student Assessment methods
  • Oral Exams (Summative)
  • Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
Δ. Μπετσάκος, Εισαγωγή στην Πραγματική Ανάλυση, Εκδόσεις Αφοί Κυριακίδη, 2016.
Additional bibliography for study
1. Gerald B. Folland, Real Analysis (Modern Techniques and Applications), Wiley Interscience, second ed. 1999. 2. Σημειώσεις Θεωρίας Μέτρου του Μιχ. Παπαδημητράκη (αγγλικά). 3. Σημειώσεις Θεωρίας Μέτρου του Απ. Γιαννόπουλου.
Last Update
13-03-2020