Difference between revisions of "Math 641: Functions of a Real Variable"
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#* Measurable spaces | #* Measurable spaces | ||
#* Measure spaces | #* Measure spaces | ||
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#* Abstract measurable mappings | #* Abstract measurable mappings | ||
#* Measurable real- and extended-real-valued functions | #* Measurable real- and extended-real-valued functions | ||
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#* Integrating nonnegative functions | #* Integrating nonnegative functions | ||
#* Integrating L<sup>1</sup> functions | #* Integrating L<sup>1</sup> functions | ||
| + | #* Monotone Convergence Theorem | ||
| + | #* Fatou's Lemma | ||
| + | #* Dominated Convergence Theorem | ||
| + | #* Effect of sets of measure zero | ||
# Product Measures | # Product Measures | ||
# Differentiation and integration | # Differentiation and integration | ||
Revision as of 17:21, 13 August 2008
Contents
Catalog Information
Title
Functions of Real and Complex Variables 1.
Credit Hours
3
Prerequisite
Math 542 or instructor's consent
Description
Fundamentals of measure and integration, Borel measures, product measures, L^ spaces, introduction to functional analysis, Radon Nikodym theorem, differentiation theory, Fourier transforms.
Desired Learning Outcomes
Prerequisites
Minimal learning outcomes
- Abstract measure theory
- σ-algebras
- Measures
- Positive measures
- Signed measures
- σ-finite measures
- Measurable spaces
- Measure spaces
- Abstract integration theory
- Abstract measurable mappings
- Measurable real- and extended-real-valued functions
- Integrating simple functions
- Integrating nonnegative functions
- Integrating L1 functions
- Monotone Convergence Theorem
- Fatou's Lemma
- Dominated Convergence Theorem
- Effect of sets of measure zero
- Product Measures
- Differentiation and integration
- Miscellaneous
- Borel sets
