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Ergodic Theory of Groups, SS 2020
Prof. Dr. C. Löh / J. WitzigCorrection log for the lecture notes:
| Date | Page | Correction |
| 22.04.2020 | A.5 | Added Hausdorff hypothesis to Definition of outer Radon measure |
| 29.04.2020 | 13 | Proposition 1.2.9, part 2: "irrational" corrected to "rational" |
| 03.05.2020 | 9 | Remark 1.1.7: added second countability assumption |
| 07.05.2020 | 33 | Theorem 1.3.8: corrected two typos in the proof (a sign in the definition of \mu_n and an exponent in the last line) |
| 07.05.2020 | 41 | Proposition 1.4.24: corrected the inconsistent use of A and B in the proof |
| 12.05.2020 | Week 4 | Exercise 3.3: clarified "natural numbers" |
| 19.05.2020 | 53 | Proposition 2.1.8: emphasised that the group needs to be infinite |
| 19.05.2020 | Week 5 | Exercise 4.1: Introduced \gamma. |
| 20.05.2020 | Week 6 | Exercise 5.3: Added mixing hypothesis for \beta. |
| 26.05.2020 | 62 | Definition 2.1.27: invariant vectors should be non-zero |
| 26.05.2020 | 69 | Quick check 2.2.8: Added missing reference. |
| 26.05.2020 | 73 | proof of the maximal ergodic theorem: Added missing \mu(E_\alpha) [twice]. |
| 03.06.2020 | 68 | Added a comment about proving the L^1-version via L^\infty or via L^2 |
| 03.06.2020 | 76 | Definition 2.2.17, part 1: corrected d-adic expansion |
| 04.06.2020 | A.10 | Example A.1.30: corrected the conditional expectations |
| 05.06.2020 | 72/Week 7 | Proposition 2.2.12/Exercise 6.3: changed summation range in definition of g_n |
| 05.06.2020 | Week 7 | Exercise 6.4: corrected definition of r_A (only n > 0 should be considered) |
| 12.06.2020 | 92 | Definition 3.1.1: Added the measurability condition for R |
| 12.06.2020 | 98 | Definition 3.1.16: One of the f's was supposed to be a g. |
| 12.06.2020 | 101 | Figure 3.1: Now the phi's can actually be bijections. |
| 16.06.2020 | 97/98 | Proof of Proposition 3.1.13: For non-free actions, we have to be more careful to make the A_\gamma pairwise disjoint. |
| 16.06.2020 | 102 | Example 3.2.5: For the parts on the Cayley graphs, we need freeness. |
| 23.06.2020 | 115 | The \phi_{\theta,j} are from \Omega (not from \Theta_0 \cup \Theta_0^{-1}. This is also corrected in the notes (p. 5, in "green"). |
| 24.06.2020 | Exercise 10.4: URL corrected | |
| 30.06.2020 | 137 | Corollary 3.3.27: replaced cost by cost -1. |
| 01.07.2020 | 129/130 | Proof of Proposition 3.3.15: uses free actions now instead of essentially free actions (to avoid complications in the ergodic decomposition argument) |
| 02.07.2020 | 129/Week 12 | Lemma 3.3.16/Exercise 11.2: Added the missing freeness condition. |
| 04.07.2020 | notes 30.06. | The "open" problem was not open. |
| 08.07.2020 | 148 | 2 => 1: added missing integral |
| 10.07.2020 | 138 | Quick check 3.3.30: corrected the computations involving rg F_2 |
| 18.07.2020 | 153 | Theorem 4.2.8: In general, A is not a strict section (but meets only almost every orbit). |
| 21.07.2020 | 168 | first line: added "\perp" |
| 22.07. | 175 | Outlook 5.3.2: rg \pi_1 (M) instead of rg M |
| 22.07. | 176/177 | proof of Theorem 5.3.7: 1/v_3 instead of v_3 (twice) |
| 29.07. | 19 | Exercise 1.2.25: index typo |
| 29.07. | 70 | Quick check 2.2.8, part 2: factor n instead of 1/n |
| 29.07. | 84 | Corollary 2.3.7, proof of part 2: typos in formulas |
| 29.07. | 118 | Theorem 3.2.34: "essentially free" was missing as hypothesis |
| 29.07. | 119 | Example 3.2.37: typo in subscript |
| 29.07. | 138 | Quick check 3.3.30, part 2: 0+0+1 is now 1 :) |
| 29.07. | 162 | Theorem 4.3.3: "S" instead of "K" |