Errata

p. 81: line 9: replace 1025/(N+1024) by 1024/(N+1023).
p. 81: line 11: tighten up the "1,000,000" (the spaces are too large after each of the two commas)

p. 188: line -5: It should be "Arntzenius" (with an "n"), not "Artzenius".

p. 283: line 10: replace "for propositional logic is given by the two axioms" by "for propositional logic with connectives $\rimp$ and $\neg$ is given by the three axioms". Then remove the comma after the two displayed formulas, and add the following formula to the list: (\neg \phi \rimp \psi) \rimp ((\neg \phi \rimp \neg \psi) \rimp \phi), Finally, replace A completeness proof can be found in \cite{Popkorn}\index{Popkorn, S.}. by Mendelson [1997] provides a completeness proof. Later, on line -9, replace "[Hughes and Creswell 1968], [Chellas 1980], ... [Blackburn, de Rijke, and Venema 2001]." by "[Blackburn, de Rijke, and Venema 2001; Chellas 1980; Hughes and Cresswell 1968; Popkorn 1994]."

p.8: line -5: devotedx -> devoted

p. 15: line 8: add "(finite)" in parens before union<
p. 15: line -10: again, add "(finite) in parens before union at the beginning of the line. Rewrite the next sentence (which starts ("This is no longer ...") as follows: "However, if $W$ is infinite, it may not be the case that every set in $\F$ is a countable union of basic sets.

p.28: line -10: In the definition of V_1, the union should be over B in \F, not \F'. Similarly, on the next line, in the definition of V_2, the intersection should be over B in \F.

p. 30: In equation (2.9), it should be less than or equal to, not greater than or equal to.

p. 31: line 11: all inner measures satisfy (2.8), not (2.12)

p. 34: line 1; Just as in equation (2.9), it should be less than or equal to, not greater than or equal to.

p. 56: line 4: add the word "countable" before union
p. 56: line 6: add the word "finite" before union

p.74: line 6: BH should be BT

p. 78: line 14: In bet B1, replace N(\overline{U}, 1 - \beta_2) by N(U \inter V, 1-\beta_3). In B2, replace N(U,\beta_2) by N(\overline{U \inter V}, \beta_3).

p. 127: line -3: In Lemma 4.3.3, you should also assume that V \inter U' \in \F'.

p. 128: line 10: There are extra set braces in the definition of \F'

p. 172: In the definition of "multiplication" for regret, t should say that x \otimes y = \infty (that's Latex for "x circle-times y = infinity"), not x \otimes y = 0!

p. 180: Exercise 5.8: the four subscripts on the second line should be \P, not \mu.
p. 180: Exercise 5.9: add "if c > 0" after "E(cX) = c E(X)". Then two lines later, it should say that the latter three properties provide an alternate characterization of lower expectation (not of \le_\P).

p. 193: line -2: it should be \PR_2(w_3), not \PR_1(w_3); similarly, on line -1, it should be \PR_2(w_4), not \PR_1(w_4).

p. 195: line -4: much like the typos on p. 193, it should be \K_2(w_3) and \K_2(w_4), not \K_1(w_3) and \K_1(w_4)

p. 201: line -5: Missing right paren at the end of \mu_{\R,i}

p. 205: add "U is a subset of \K_i(r,m_1)" to the assumptions in Proposition 6.4.3.

p. 211: line 11: "the true world" is missing after "where w_0"

p. 216: lines 15-16: You *gain* by switching if the goat is behind the door you've picked; otherwise you lose.