MAST 669
Measure Theory
Fall 2026
Topics
- Outer measure, Lebesgue measure and positive measures
- Lebesgue integration and convergence theorems
- Differentiation and maximal functions
- Lebesgue Lp spaces
- Product measures
- Real and complex measures
- Radon–Nikodym theorem
Readings
- Listed textbook (requirement not stated): S. Axler. Measure, Integration & Real Analysis. Springer, 2020. https://measure.axler.net/
- Other textbook (requirement not stated): E. M. Stein and R. Shakarchi. Real Analysis, Measure Theory and Integration. Princeton University Press, 2005.
- Other textbook (requirement not stated): E. M. Stein and R. Shakarchi. Functional Analysis. Princeton University Press, Macmillan, 2011.
- Other textbook (requirement not stated): G. B. Folland. Real Analysis: Modern Techniques and Their Applications. Wiley, 2013.
- Other textbook (requirement not stated): H. L. Royden. Real Analysis, 3rd or 4th edition.
Fall 2024 · MATH 467
Readings
- Measure, Integration & Real Analysis, by S. Axler, Springer, 2020.
- Real Analysis, Measure Theory and Integration, by E.M. Stein and R. Shakarchi, Princeton University Press, 2005.
- Functional Analysis, by E.M. Stein and R. Shakarchi, Princeton University Press, Macmillan, 2011.
- Real Analysis: Modern Techniques and Their Applications, by G.B. Folland, Wiley, 2013.
- Real Analysis, by H.L. Royden (3rd or 4th Edition).
Winter 2024 · MATH 467
Readings
- Measure, Integration & Real Analysis, by S. Axler, Springer, 2020.
- Real Analysis, by H.L. Royden (3rd or 4th Edition).
- Real Analysis, Measure Theory and Integration, by E.M. Stein and R. Shakarchi, Princeton University Press, 2005.
- Functional Analysis, by E.M. Stein and R. Shakarchi, Princeton University Press, Macmillan, 2011.
- Real Analysis: Modern Techniques and Their Applications, by G.B. Folland, Wiley, 2013.
Winter 2023 · MATH 467
Readings
- Measure, Integration & Real Analysis, by S. Axler, Springer, 2020.
- Real Analysis, by H.L. Royden (3rd or 4th Edition).
- Real Analysis, Measure Theory and Integration, by E.M. Stein and R. Shakarchi, Princeton University Press, 2005.
- Functional Analysis, by E.M. Stein and R. Shakarchi, Princeton University Press, Macmillan, 2011.
Winter 2022 · MATH 467
Readings
- Measure, Integration & Real Analysis, by S. Axler, Springer, 2020.
- Real Analysis, by H.L. Royden (3rd or 4th Edition).
- Real Analysis, Measure Theory and Integration, by E.M. Stein and R. Shakarchi, Princeton University Press, 2005.
- Functional Analysis, by E.M. Stein and R. Shakarchi, Princeton University Press, Macmillan, 2011.
Sources
- Course catalogue ↗2026–2027
- Syllabus or course outline ↗Fall 2026
- Historical course outline ↗Fall 2024
- Historical course outline ↗Winter 2024
- Historical course outline ↗Winter 2023
- Historical course outline ↗Winter 2022
- Fall 2026 outline. Course header explicitly lists MATH 467, MAST 669, MAST 837. The “Other Textbooks” list is not labelled required; publisher wording is preserved as printed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.