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Department: Mathematics

(Graduate program)

Department/Program Objectives:

Courses on the Web:


Course code: MATH-501

Course name: Real Analysis - I
Instructor: Assoc. Prof. Dr. Alexandre Gontcharov
Credits: 3
ECTS Credits: 6
Academic Year: 2009-2010
Semester: Fall
Prerequisites:
Course web site:
Course description:
Concepts of integration. Henstock-Kurzweil integral. Borel sets, Bair functions. Outer measures. Measurable sets. Lebesgue and Lebesgue-Stieltjes measures. Lebesgue density theorem. Hausdorff measures and Hausdorff dimension. Measurable functions. Lusin’s and Egorov’s theorems. Convergence in measure. Lebesgue integral. Basic theorems of Lebesgue integral. Modes of convergence. Differentiation of indefinite Lebesgue integral. Signed measures. The Radon- Nikodym theorem. Product measures. Spaces of integrable functions.
Videos:

Short description: Hiebert Spaces
Long description:
Recorded on: 2009-12-29
Video File: [mp4] [mov]

Short description: Riesz' Representation Theorem
Long description:
Recorded on: 2009-12-28
Video File: [mp4] [mov]

Short description: Approximation in LP
Long description:
Recorded on: 2009-12-22
Video File: [mp4] [mov]

Short description: Rearrangement of Functions
Long description:
Recorded on: 2009-12-22
Video File: [mp4] [mov]

Short description: Spaces of Integrable Functions
Long description:
Recorded on: 2009-12-21
Video File: [mp4] [mov]

Short description: Applications of Fubini Theorem
Long description:
Recorded on: 2009-12-15
Video File: [mp4] [mov]

Short description: Fubini Theorem
Long description:
Recorded on: 2009-12-15
Video File: [mp4] [mov]

Short description: Product Measures
Long description:
Recorded on: 2009-12-14
Video File: [mp4] [mov]

Short description: Radon-Nikodym Theorem
Long description:
Recorded on: 2009-12-08
Video File: [mp4] [mov]

Short description: Hahn Decomposition
Long description:
Recorded on: 2009-12-08
Video File: [mp4] [mov]

Short description: Signed Measures
Long description:
Recorded on: 2009-12-07
Video File: [mp4] [mov]

Short description: Absolutely Continuous Functions
Long description:
Recorded on: 2009-12-01
Video File: [mp4] [mov]

Short description: Indefinite Lebesgue Integral
Long description:
Recorded on: 2009-12-01
Video File: [mp4] [mov]

Short description: Differentiation of Monotone Function
Long description:
Recorded on: 2009-11-17
Video File: [mp4] [mov]

Short description: Indefinite Lebesgue Integral
Long description:
Recorded on: 2009-11-17
Video File: [mp4] [mov]

Short description: Characterizations of Integrability
Long description:
Recorded on: 2009-11-16
Video File: [mp4] [mov]

Short description: Lebesgue Dominated Convergence Theorem
Long description:
Recorded on: 2009-11-10
Video File: [mp4] [mov]

Short description: Fatou Lemma
Long description:
Recorded on: 2009-11-10
Video File: [mp4] [mov]

Short description: Monotone Convergence Theorem
Long description:
Recorded on: 2009-11-09
Video File: [mp4] [mov]

Short description: Lebesgue integral for bounded functions
Long description:
Recorded on: 2009-11-03
Video File: [mp4] [mov]

Short description: Convergence in measure
Long description:
Recorded on: 2009-11-03
Video File: [mp4] [mov]

Short description: Lusin theorem
Long description:
Recorded on: 2009-11-02
Video File: [mp4] [mov]

Short description: Egorovs theorem
Long description:
Recorded on: 2009-10-27
Video File: [mp4] [mov]

Short description: Almost uniform convergence
Long description:
Recorded on: 2009-10-27
Video File: [mp4] [mov]

Short description: Review of mid-term exam
Long description:
Recorded on: 2009-10-26
Video File: [mp4] [mov]

Short description: Measurable functions
Long description:
Recorded on: 2009-10-20
Video File: [mp4] [mov]

Short description: Nonmeasurable sets
Long description:
Recorded on: 2009-10-20
Video File: [mp4] [mov]

Short description: Extension of premeasures
Long description:
Recorded on: 2009-10-19
Video File: [mp4] [mov]

Short description: Hausdorff measures
Long description:
Recorded on: 2009-10-13
Video File: [mp4] [mov]

Short description: Lebesgue density theorem
Long description:
Recorded on: 2009-10-13
Video File: [mp4] [mov]

Short description: Approximation of measurable sets
Long description:
Recorded on: 2009-10-12
Video File: [mp4] [mov]

Short description: Lebesgue measure
Long description:
Recorded on: 2009-10-06
Video File: [mp4] [mov]

Short description: Measurable sets
Long description:
Recorded on: 2009-10-06
Video File: [mp4] [mov]

Short description: Concept of measure
Long description:
Recorded on: 2009-10-05
Video File: [mp4] [mov]

Short description: Baire functions
Long description:
Recorded on: 2009-09-29
Video File: [mp4] [mov]

Short description: Borel sets
Long description:
Recorded on: 2009-09-29
Video File: [mp4] [mov]

Short description: Category
Long description:
Recorded on: 2009-09-28
Video File: [mp4] [mov]