| Area of Mathematics: | Analysis | ||
| Semester: | 6ο | ||
| Course ID: | 61101 | ||
| Course Type: | Compulsory | ||
| Teaching hours per week: | Theory: 4 | Practice: 2 | Laboratory: 0 |
| ECTS : | 7 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Tsirivas Nikolaos |
Description
- Algebras, σ-Algebras, Borel sets, examples, σ-Algebra of Borel sets in R and R2.
- Measures, properties of measures, finite measures, null sets, complete measures.
- Outer measure, measurable sets of an outer measure, Caratheodory’s Theorem.
- Outer Lebesque measure, Lebesque measure, Lebesque measurable sets in R and R2
- Lebesque measurable functions.
- The Lebesque integral.
- Basic convergence theorems. Comparison of Lebesque integral with Riemann integral.
- Product measures, Fubini’s theorem.
- Sequences of measurable functions, spaces.
Bibliography
D.Cohn , Measure Theory , Birkhauser , Boston , 1980 .
P.Halmos , Measure Theory , Van Nostrand , Princeton , 1950 .
