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PMATH 650

Measure Theory

Graduate

Fall 2024 · Lebesque Integration and Fourier Analysis

Topics

  • Vector-valued Riemann integration
  • Lebesgue measure and integration
  • Lp spaces
  • Hilbert spaces
  • Fourier analysis

Readings

  • Course notes available from L. W. Marcoux’s teaching page: https://www.math.uwaterloo.ca/~lwmarcou/
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Fall 2023 · Lebesgue Integration and Fourier Analysis

Topics

  • We will cover the following material from the textbook Sections 1.1–1.4. 1.6–1.12, 1.15–1.20: Preview of Integration Sections 2.1, 2.8, 2.10: Lebesgue Measure Sections 4.1, 4.2, 5.1–5.4: Lebesgue Measurable Functions and Lebesgue Integration Sections 13.1–13.4, 13.8: The L p Spaces Sections 12.1, 12.3, 12.11, 14.1–14.4: Banach and Hilbert Spaces Sections 15.1–15.5, 15.9, 15.11: Fourier Series

Readings

  • Real Analysis, by A.Bruckner, J.Bruckner and B.Thomson, can be purchased in paperback form, or downloaded free in pdf form, at http://ClassicalRealAnalysis.info
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Undated · Measure Theory and Fourier Analysis

Topics

  • Lebesgue Measure
  • Lebesgue Integration
  • The Lp Spaces
  • Banach and Hilbert Spaces
  • Fourier Series

Readings

  • Chapter 1. Lebesgue Measure — https://www.math.uwaterloo.ca/~snew/PMATH450/chap1.pdf
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  • Chapter 2. Lebesgue Integration — https://www.math.uwaterloo.ca/~snew/PMATH450/chap2.pdf
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  • Chapter 3. The Lp Spaces — https://www.math.uwaterloo.ca/~snew/PMATH450/chap3.pdf
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  • Chapter 4. Banach and Hilbert Spaces — https://www.math.uwaterloo.ca/~snew/PMATH450/chap4.pdf
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  • Chapter 5. Fourier Series — https://www.math.uwaterloo.ca/~snew/PMATH450/chap5.pdf
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  • Appendix. PMATH 351 Notes — https://www.math.uwaterloo.ca/~snew/PMATH450/PMATH351Notes.pdf
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Sources