Math 641: Functions of a Real Variable

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Catalog Information


Functions of Real and Complex Variables 1.

Credit Hours



Math 542 or instructor's consent


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


Minimal learning outcomes

  1. Measure theory
    • σ-algebras
    • Measures
    • Measurable spaces
    • Measure spaces
  2. Integration theory
    • Abstract measurable mappings
    • Measurable real- and extended-real-valued functions
  3. Product Measures
  4. Differentiation and integration

Additional topics

Courses for which this course is prerequisite