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Department:

MATH

Course Number:

6579

Hours - Lecture:

3

Hours - Lab:

0

Hours - Recitation:

0

Hours - Total Credit:

3

Typical Scheduling:

Even Fall Semesters

An introduction to measure theory and Lebesgue integration with a focus on topics that tend to be of the most utility in science and engineering. The three course series MATH 6579, 6580, and 6221 is designed to provide a high level mathematical background for engineers and scientists.

This course is equivalent to MATH 6337. Students should not be able to obtain credit for both MATH 6579 and MATH 6337.

Prerequisites:

MATH 4317.

Course Text:

At the level of Bartle, “The Elements of Integration and Lebesgue Measure”, or Heil lecture notes, “Real Analysis for Engineers”.

Topic Outline:

- Review of background.
- Exterior measure and Lebesgue measure on |R.
- Lebesgue integration on |R: measurable functions, convergence in measure, Lebesgue integral, Monotone Convergence Theorem, Fatou’s Lemma, Dominated Convergence Theorem, Fubini’s Theorem.
- Abstract measure theory, including:
- Sigma-algebras and measurability.
- Outer measures and premeasures.
- Integration and convergence theorems.
- Radon–Nikodym Theorem.
- Caratheodory Extension Theorem.