## Lower Previsions: The Book

### Errata

• p10, line above Definition 1.14: "μ(A)⊆μ(B)" should be "μ(A)≤μ(B)"
• p31: The text says that Walley's 2000 notion of desirability captures a weak preference to the zero gamble, whilst his 1991 notion captures strong preference. It must be the other way around: "Our notion of acceptability coincides with Walley's earlier (1991, Appendix F) notion of desirability, also used by Moral (2000) and Couso and Moral (2009, 2011), and aims at capturing a weak preference to the zero gamble. Walley in his later paper (2000, p. 137) and also Moral (2005) use a slightly different notion of acceptability, which is rather aimed at representing a strict preference to the zero gamble."
• p38, middle of page: "Similarly, upr(D)(f) is the *infimum* price"
• p42: The inequality just before Definition 4.4 must be reversed: "P̲(f)≤Q̲(f)"
• p44, line 2: "j∈{1, ..., n}" should be "i∈{1, ..., n}"
• p45, paragraph before 4.2.4: "transacttion" should be "transaction"
• p47, Definition 4.10(D): "bounded gambles f₀, ..., fₘ" should be "bounded gambles f₀, ..., fₙ"
• p48, 2nd line of (C)=>(D): "bounded gambles f₀, ..., fₘ" should be "bounded gambles f₀, ..., fₙ"
• p123, line just above equation (7.2): "p̲(A)" should be "p̲(x)"
• p233, fourth last line: "... that the subject is practically *certain* will only ..."
• p283, Theorem 13.53, item (iv) should be instead: "For all non-empty events A there is a gamble f such that -∞<E̲(f|A)<+∞."
• p284-285, proof of Theorem 13.53 (iv) => (i): The last step of the proof (going from (13.28) to the equation on the page 285) is wrong. To fix the proof, choose A to be the union of C₁, ..., Cₚ and assume that E̲(f|A)>-∞. Now you can easily prove that E̲(f|A)=+∞.
• p375, last paragraph: the phrases "all measurable bounded gambles are integrable" and "equivalence of Lebesgue integration and natural extension" should appear between brackets
• p396, fourth entry: gamble -> Gamble