Page 4, part (iv) of (1.1): inequality goes the wrong direction. Page 4, line -3: last y should be an x. Page 12, (3.1a): superfluous "If". Page 43: reference to exercise 3.10 of Chapter 2 (two thirds of the way down the page) should be to Exercise 3.23. Page 17 in the remark: Probably there should be an argument "(y)" at the end of the equation. Page 95 line 1: add "for x \in h Z" at the end of first line. Page 123 line 1-2: proof box at end of line 2 should be at end of line 1. Page 135, line -4: period should be a comma. Page 158: Example should be numbered 7.5, not 7.4. Page 158 in (7.17): "$t^{3/2}$" should be "$t^{2/3}$". Page 160, last line: $-\epsilon^2$ should be $-\epsilon^{-2}$. Page 198: the sentence just before (3.6) is probably meant to go just before Theorem (3.7). Page 200, fourth line of the proof: $1 < k < n$ should be $1 \leq k < n$. Page 243, top: $P(X = \infty) = 0$ is not the right reason to cite since it has not been shown for $\nu$: $\P$ refers to $\mu$, with respect to which $\{X=\infty\}$ always has probability 0. Instead, need to argue that $L^1$-convergence implies $P(X = 0)$ is not equal to 1, hence by dichotomy $\P (X=0) = 0$, which now implies mutual absolute continuity. Page 250, line 9: parentheses needed around (p-1) in the denominator. Page 253: Reference to Kronecker's Lemma at the end of the proof of (4.10) should be to (8.5) of Chapter 1, not (8.1) of Chapter 1. Page 254, line 5: displayed equation is missing a period at the end. Page 306, Example 4.7: the exercise referred to should be 3.10, not 3.9. Page 307, section header at top of page: changes to Section 5.5 a page too early. Page 374, line 4 from bottom: $t \mapsto \Omega (t)$ should be $\omega \mapsto \omega (t)$. Page 375, proof of Theorem (1.5): \eta is not really needed. Page 377, header: Still in Section 7.1, not Section 7.2. Page 430, equation (8.11): a factor of $2 \cdot (-1)^m$ is missing from the summand. Also, what happened to figure 7.8.1 from the second edition? Page 430, line after equation (8.11): missing "o" in "Kolmogorov". Page 459, in Exercise 4.3: j_m should be a_j. Page 465: page header indicating name of the current section changes to A6 a page too early. Page 477: space should go after comma, not before (first line) Page 493: page references to branching processes are missing p. 243. Page 494: the change of variables formula is on page 17, not page 16.