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

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(Minimal learning outcomes)
(Minimal learning outcomes)
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# Measure theory
+
# Abstract measure theory
 
#* σ-algebras
 
#* σ-algebras
 
#* Measures
 
#* Measures
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#* Measurable spaces
 
#* Measurable spaces
 
#* Measure spaces
 
#* Measure spaces
# Integration theory
+
# Abstract integration theory
 
#* 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 16:21, 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. Abstract measure theory
    • σ-algebras
    • Measures
      • Positive measures
      • Signed measures
      • σ-finite measures
    • Measurable spaces
    • Measure spaces
  2. 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
  3. Product Measures
  4. Differentiation and integration
  5. Miscellaneous
    • Borel sets

Additional topics

Courses for which this course is prerequisite