Ernst Hansen: Measure Theory List of relevant errors

Ernst Hansen: Measure Theory
Third Edition
List of relevant errors
October 28, 2008
EH
This is a list of the errors in Ernst Hansen: Measure theory, third edition,
deemed to be a potential source of confusion.
100 7 Original: then the function x ↦→ lim sup n∈N fn(x) is also an Mfunction.
Correct: then the function x ↦→ lim sup n→∞ fn(x) is also an Mfunction.
Reported by: Niels Richard Hansen
138 9 Original: 6.2 Let f ∈ M + (R, B) be a non-negative measurable
function.
Correct: 6.2 Let f ∈ M + (R, B) be a non-negative measurable
function.
Reported by: Magnus Tor Ry Hessler
139 8 Original:
Correct:
µ ({x|X | f(x) = ∞}) = 0 .
µ ({x ∈ X | f(x) = ∞}) = 0 .
Reported by: Magnus Tor Ry Hessler
1

1692 Original: We see by the collage lemma that f has measurable
sections,
Correct: We see by lemma 4.11 that f has measurable sections,
Reported by: Niels Richard Hansen
171 1 Original: We see by the collage lemma that f has measurable
sections,
Correct: We see by lemma 4.11 that f has measurable sections,
Reported by: Niels Richard Hansen
174 ′′ 7 Original: Next, consider two H-sets G1⊆G2.
Correct: Next, consider two H-sets G1 ⊂ G2.
Reported by: Magnus Tor Ry Hessler
17411 Original: Assume that G1⊆G2⊆... is an increasing sequence of
H-sets,
Correct: Assume that G1 ⊂ G2 ⊂ . . . is an increasing sequence of
H-sets,
Reported by: Magnus Tor Ry Hessler
194 10 Original:
µ1⊗. . .⊗µn(A1×. . .×An) =
for Ai ∈ Ei, i = 1, . . .,n.
Correct:
µ1⊗. . .⊗µn(A1×. . .×An) =
n�
µi(Ai) for A1 ∈ E1, . . .,An ∈ En ,
i=1
n�
µi(Ai) for A1 ∈ E1, . . .,An ∈ En .
i=1
Reported by: Magnus Tor Ry Hessler
2

19710 Original: �
−e −x − 1
2 e−2x
�∞ 0
Correct: �
−e −x + 1
2 e−2x
�∞ 0
Reported by: Magnus Tor Ry Hessler
1971 Original: as we saw in theorem 2.21,
Correct: as we saw in lemma 2.21,
Reported by: Magnus Tor Ry Hessler
201 12 Original: Interchanging the order of integration in successive integrals
cannot be performed freely if the integrand is non-negative
Correct: Interchanging the order of integration in successive integrals
cannot be performed freely unless the integrand is nonnegative
Reported by: Ninna Reitzel Jensen
2011 Original:
Correct:
y ↦→ a coste −ty + b sin t e −ty ,
t ↦→ a coste −ty + b sin t e −ty .
Reported by: Magnus Tor Ry Hessler
3

30812 Original: The coefficients of the power series (14.2) are nonnegative
Correct: The coefficients of the power series (14.3) are nonnegative
Reported by: Ninna Reitzel Jensen
30812 Original: The coefficients of the power series (14.2) are nonnegative
Correct: The coefficients of the power series (14.3) are nonnegative
Reported by: Ninna Reitzel Jensen
360 5 Original: �
Correct: �
�
|X| dP =
�
|X| dP =
(|X|≤C)
(|X|≤C)
Reported by: Magnus Tor Ry Hessler
392 7 Original: for some n ∈ N.
Correct: for some n = 2, 3, . . ..
Reported by: Ernst Hansen
4
X dP
|X| dP

49511 Original:
Correct:
tn(x1, . . .,xn) ∈ S(N, n) for (x1, . . ., xN) ∈ X n ,
tn(x1, . . .,xn) ∈ S(N, n) for (x1, . . ., xn) ∈ X n ,
Reported by: Tilde Stadel Borum
5684 Original: The last inequality is due to the continuity of fN,
Correct: The last equality is due to the continuity of fN,
Reported by: Kang Li
5