Difference between revisions of "Math 641: Functions of a Real Variable"
From MathWiki
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#* σ-algebras | #* σ-algebras | ||
#* Measures | #* Measures | ||
| + | #** Positive measures | ||
| + | #** Signed measures | ||
| + | #** σ-finite measures | ||
#* Measurable spaces | #* Measurable spaces | ||
#* Measure spaces | #* Measure spaces | ||
| Line 27: | Line 30: | ||
#* Abstract measurable mappings | #* Abstract measurable mappings | ||
#* Measurable real- and extended-real-valued functions | #* Measurable real- and extended-real-valued functions | ||
| + | #* Integrating simple functions | ||
| + | #* Integrating nonnegative functions | ||
| + | #* Integrating L<sup>1</sup> functions | ||
# Product Measures | # Product Measures | ||
# Differentiation and integration | # Differentiation and integration | ||
| + | # Miscellaneous | ||
| + | #* Borel sets | ||
</div> | </div> | ||
Revision as of 17:19, 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
- Measure theory
- σ-algebras
- Measures
- Positive measures
- Signed measures
- σ-finite measures
- Measurable spaces
- Measure spaces
- Integration theory
- Abstract measurable mappings
- Measurable real- and extended-real-valued functions
- Integrating simple functions
- Integrating nonnegative functions
- Integrating L1 functions
- Product Measures
- Differentiation and integration
- Miscellaneous
- Borel sets
