Difference between revisions of "Math 641: Functions of a Real Variable"

From MathWiki
Jump to: navigation, search
(Minimal learning outcomes)
(Minimal learning outcomes)
Line 22: Line 22:
 
#* 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 16:19, 13 August 2008

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

  1. Measure theory
    • σ-algebras
    • Measures
      • Positive measures
      • Signed measures
      • σ-finite measures
    • Measurable spaces
    • Measure spaces
  2. Integration theory
    • Abstract measurable mappings
    • Measurable real- and extended-real-valued functions
    • Integrating simple functions
    • Integrating nonnegative functions
    • Integrating L1 functions
  3. Product Measures
  4. Differentiation and integration
  5. Miscellaneous
    • Borel sets

Additional topics

Courses for which this course is prerequisite