- Wednesday 29 November. Finished the proof of the RN Theorem; The Lebesgue decomposition; and existence of conditional expectations.
- Wednesday 15 November. Finished our discussion of Section 16. Began Section 18.
- Monday 27 November. Theorem 8.11 (the Radon-Nikodym derivative).
- Notes updated Friday 17 November at 10:05 am. Fixed a typo (added the condition that \( \rho \) omit the value \( +\infty \) at the relevant point) in the discussion of the definition of totally positive.
- Monday 20 November. Continued in Section 18, from the proof Theorem 18.5 through the definition of mutually singular.
- Friday 17 November. Homeworks 10 and 11 were due. Continued in Section 18, starting with the definition of signed measure up through Lemma 18.6.
- Monday 13 November. Finished Section 15 starting with Fubini’s Theorem. Began (what will be a brief discussion of) Section 16.
- Notes updated 8 November at 1:20 pm. Fixed typos in the proof of Theorem 15.7 (passage from finite measures to the sigma-finite case). Other small fixes and upgrades.
- Wednesday 8 November. Continued in Section 15, from Corollary 15.8 through the complete version of Tonelli’s Theorem.
- Monday 6 November. Finished the proof of Theorem 15.7. Discussed Problem 19.3 and Example 15.9.
- Friday 3 November. Homework 9 was due. More of Section 15, from Remark 15.3 to part way through the proof of Theorem 15.7 (existence of product measure).
- Notes updated Friday 3 November at 9:05am. Typos fixed and corrections and upgrades to the proof of the monotone class theorem.
- Wednesday 1 November. A brief discussion of the Riesz-Markov Theorem (Section 14). Began Section 15 up through Lemma 15.2.
- Monday 30 October. Propositions 12.17 and 12.18.
- Friday 27 October. Started Section 12.3 on uniform integrability, covering up through Lemma 12.15.
- Wednesday 25 October. Covered from Definition 12.6 (Cauchy in measure) through Proposition 12.10 (completeness of \( L^1(\mu)\)).
- Monday 23 October. Professor Jury subsituted. Discussed the typewriter sequence (Example 12.5), finished the discussion of Proposition 12.3, cover Proposition 12.2.
- Friday 20 October. Homework 8 was due. Reviewed the proof of the DCT and finished Section 11. Began Section 12 with Definitions 12.1 and an initial discussion of Proposition 12.3.
- Notes last updated Friday 20 October. Typos fixed etc.
- Wednesday 18 October. Began Section 11, covering up through the Dominated Convergence Theorem (DCT).
- Monday 16 October. Finished Section 10, starting with a review of the last bit of the MCT.
- Friday 13 October. Homework 7 was due. Proposition 9.3 through Theorem 10.3 (MCT).
- Wednesday 11 October. Finish Section 8 starting with Theorem 8.20. Begin Section 9.
- Notes updated Monday 9 October at 9:50 am. Small expository upgrades in Section 8, including the new Proposition 8.13 (before implicit in other results). Some typos fixed.
- Monday 9 October. Homework 6 was due. Finished Theorem 8.14 and continued in Section 8 up through Proposition 8.19.
- Friday 6 October. Homecoming. No class.
- Wednesday 4 October. Continued in Section 8, from Example 8.10 through Theorem 8.14 (b).
- Notes updated Wednesday 4 October at 10:30 am. Fixed the proof of Theorem 8.14(c). Small upgrades and some typos fixed in Section 8 too.
- Monday 2 October. Section 8 up through Corollary 8.9.
- Friday 29 September. Homework 5 was due. Finished Section 6 and discussed Problem 7.27.
- Wednesday 27 September. Finished the proof of Proposition 6.1. Began Example 6.2.
- Notes updated Wednesday 27 September at 9:30am. Typo patrol in Section 6.
- Notes updated Monday 25 September at 12:50. Some minor expository upgrades and typos fixed in Sections 5 and 6.
- Monday 25 September. Finished Theorem 5.4, Corollary 5.5, began Section 6 up through the middle of the proof of Proposition 6.1.
- Friday 22 September. Homework 4 was due. Theorems 5.3 and most of the proof of Theorem 5.4.
- Wednesday 20 September. Further discussion of Example 4.11; finished Section 4; Definition 5.1, Example 5.2 and Problem 7.20.
- Monday 18 September. Homework 3 was due. Finished the proof of Theorem 4.5 (equivalences of items (a), (c) and (e)); items 4.6, 4.7, 4.8 and began Example 4.11.
- Friday 15 September. Theorem 4.2 through Theorem 4.5 the equivalences of conditions (a), (b) and (d).
- Wednesday 13 September. Class canceled. (Hurrican Irma.)
- Monday 11 September. Class canceled. (Hurrican Irma.)
- Friday 8 September. Class canceled. (Hurrican Irma.)
- Notes updated Wednesday 6 September at 1:20pm. A couple of typos fixed and small expository upgrades in the first part of Section 4.
- Wednesday 6 September. Discussed Homework 2. Example 3.6 and Theorem 4.1.
- Notes updated Friday 1 September at 1:05pm. Expository upgrades and a correction to Problem 7.11(c).
- Friday 1 September. Homework 2 was due. Theorem 3.3 and Lemma 3.7.
- Notes updated Wednesday 30 August at 6:20pm. A typo fixed and a few small expository upgrades.
- Wednesday 30 August. Definitions 3.1 and 3.2 and Proposition 3.4.
- Starting Monday 28 August we will meet in LIT 223.
- Monday 28 August. Homework 1 was due. Theorem 2.3 through Theorem 2.8.
- Friday 25 August. Definition 1.13 through Example 2.2.
- Wednesday 23 August. Finished Example 1.8, covered items Items 1.7, 1.9-1.12.
- Monday 21 August. Items 1.1-1.6 and 1.8(a)-(g) in the notes.
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