## Lower Previsions: The Book

This page gives some further information about the Lower Previsions book, published by myself and Gert de Cooman (Wiley Series in Probability and Statistics, 2014).

### Links

- Wiley's website has a summary, with table of contents.
- Gert's blog contains part of the preface.
- My post on the SIPTA blog has a brief history of how the book came about.

### 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