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 nonzero

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^1version via L^\infty or via L^2

03.06.2020

76

Definition 2.2.17, part 1: corrected dadic 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 nonfree 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"
