Akademik Dersler - İçerik

Will be able to recall and relate fundamental concepts in real analysis.
Explains the real number system and topological concepts.
Explains convergence in sequences and function sequences.
Explains continuity and uniform continuity.
Will be able to explain the fundamental concepts of measure theory.
EN: Defines sigma-algebras.
Explains measure and outer measure.
Explains Lebesgue outer measure.
Will be able to analyze measurable sets and functions.
Defines Lebesgue measurable sets.
Explains measurability criteria.
Analyzes measurable functions.
Will be able to use the concept of the Lebesgue integral.
Defines simple functions.
Defines the Lebesgue integral.
Analyzes integrability.
Will be able to apply convergence theorems.
States Fatou lemma.
Explains monotone convergence theorem.
Applies dominated convergence theorem.
Will be able to analyze function spaces.
Defines L^p spaces.
Explains L^1 and L^2 spaces.
Will be able to explain advanced results in measure theory.
Explains product measures.
States Fubini theorem.