Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses.

17. General Measure Spaces: Their Properties and Construction.

• 17.1. Measures and Measurable Sets. Section 17.1 notes
• Supplement. Proofs of Theorems in Section 17.1. Beamer file of Section 17.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section 17.1. Print file of Section 17.1 proofs
• 17.2. Signed Measures: The Hahn and Jordan Decompositions. Section 17.2 notes
• Supplement. Proofs of Theorems in Section 17.2. Beamer file of Section 17.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section 17.2. Print file of Section 17.2 proofs
• 17.3. The Caratheodory Measure Induced by an Outer Measure. Section 17.3 notes
• Supplement. Proofs of Theorems in Section 17.3. Beamer file of Section 17.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section 17.3. Print file of Section 17.3 proofs
• 17.4. The Construction of Outer Measures. Section 17.4 notes
• Supplement. Proofs of Theorems in Section 17.4. Beamer file of Section 17.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section 17.4. Print file of Section 17.4 proofs
• 17.5. The Caratheodory-Hahn Theorem: The Extension of a Premeasure to a Measure. Section 17.5 notes
• Supplement. Proofs of Theorems in Section 17.5. Beamer file of Section 17.5 proofs
• Supplement. Printout of the Proofs of Theorems in Section 17.5. Print file of Section 17.5 proofs
• Study Guide 17.

18. Integration Over General Measure Spaces.

• 18.1. Measurable Functions. Section 18.1 notes
• Supplement. Proofs of Theorems in Section 18.1. Beamer file of Section 18.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section 18.1. Print file of Section 18.1 proofs
• 18.2. Integration of Nonnegative Measurable Functions. Section 18.2 notes
• Supplement. Proofs of Theorems in Section 18.2. Beamer file of Section 18.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section 18.2. Print file of Section 18.2 proofs
• 18.3. Integration of General Measurable Functions. Section 18.3 notes
• Supplement. Proofs of Theorems in Section 18.3. Beamer file of Section 18.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section 18.3. Print file of Section 18.3 proofs
• 18.4. The Radon-Nikodym Theorem. Section 18.4 notes
• Supplement. Proofs of Theorems in Section 18.4. Beamer file of Section 18.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section 18.4. Print file of Section 18.4 proofs
• 18.5. The Nikodym Metric Space: The Vitali-Hahn-Saks Theorem. Section 18.5 notes
• Supplement. Proofs of Theorems in Section 18.5. Beamer file of Section 18.5 proofs
• Supplement. Printout of the Proofs of Theorems in Section 18.5. Print file of Section 18.5 proofs
• Study Guide 18.

19. General L^p Spaces: Completeness, Duality, and Weak Convergence.

• 19.1. The Completeness of L^p(X, μ), 1 ≤ p ≤ ∞ . Section 19.1 notes
• Supplement. Proofs of Theorems in Section 19.1. Beamer file of Section 19.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section 19.1. Print file of Section 19.1 proofs
• 19.2. The Riesz Representation Theorem for the Dual of L^p(X, μ), 1 ≤ p < ∞ . Section 19.2 notes
• Supplement. Proofs of Theorems in Section 19.2. Beamer file of Section 19.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section 19.2. Print file of Section 19.2 proofs
• 19.3. The Kantorovitch Representation Theorem for the Dual of L^∞(X, μ). Section 19.3 notes
• Supplement. Proofs of Theorems in Section 19.3. Beamer file of Section 19.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section 19.3. Print file of Section 19.3 proofs
• 19.4. Weak Sequential Compactness in L^p(X, μ), 1 < p < ∞ . Section 19.4 notes
• Supplement. Proofs of Theorems in Section 19.4. Beamer file of Section 19.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section 19.4. Print file of Section 19.4 proofs
• 19.5. Weak Sequential Compactness in L¹(X, μ): The Dunford-Pettis Theorem. Section 19.5 notes
• Supplement. Proofs of Theorems in Section 19.5. Beamer file of Section 19.5 proofs
• Supplement. Printout of the Proofs of Theorems in Section 19.5. Print file of Section 19.5 proofs
• Study Guide 19.

20. The Construction of Particular Measures.

• 20.1. Product Measures: The Theorems of Fubini and Tonelli. Section 20.1 notes
• Supplement. Proofs of Theorems in Section 20.1. Beamer file of Section 20.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section 20.1. Print file of Section 20.1 proofs
• 20.2. Lebesgue Measure on Euclidean Space ℝⁿ. Section 20.2 notes
• Supplement. Proofs of Theorems in Section 20.2. Beamer file of Section 20.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section 20.2. Print file of Section 20.2 proofs
• 20.3. Cumulative Distribution Functions and Borel Measures on ℝ. Section 20.3 notes (Includes the definition of the Lebesgue-Stieltjes integral.)
• Supplement. Proofs of Theorems in Section 20.3. Beamer file of Section 20.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section 20.3. Print file of Section 20.3 proofs
• 20.4. Caratheodory Outer Measures and Hausdorff Measures on a Metric Space. Section 20.4 notes
• Supplement. Proofs of Theorems in Section 20.4. Beamer file of Section 20.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section 20.4. Print file of Section 20.4 proofs
• Study Guide 20.

21. Measure and Topology.

• 21.1. Locally Compact Topological Spaces.
• 21.2. Separating Sets and Extending Functions.
• 21.3. The Construction of Radon Measure.
• 21.4. The Representation of Positive Linear Functionals on C_C(X): The Riesz-Markov Theorem.
• 21.5. The Riesz Representation Theorem for the Dual of C(X).
• 21.6. Regularity Properties of Baire Measures.
• Study Guide 21.

22. Invariant Measures.

• 22.1. Topological Groups: The General Linear Group. Section 22.1 notes
• Supplement. Proofs of Theorems in Section 22.1. Beamer file of Section 22.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section 22.1. Print file of Section 22.1 proofs
• 22.2. Kakutani's Fixed Point Theorem.
• 22.3. Invariant Borel Measures on Compact Groups: von Neumann's Theorem.
• 22.4. Measure Preserving Transformations and Ergocity: The Bogoliubov-Krilov Theorem.
• Study Guide 22.

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