| Page | Line | Change |
|---|---|---|
| various | various | The printer (TechBooks) increased the thickness of some lines in some of the figures, but not uniformly, without informing us or Cambridge. Here is a list of the affected figures and a link to the original (correct) versions. |
| various | various | The changes to the lines described above appears to have also affected some fraction bars and overlines, which are now dashed or broken. Here is a list of the affected pages: 38, 118, 131, 190, 235, 295, 445, 475, 488. |
| xv | 9b | P. Poggi-Corradini (misspelled) |
| 12 | 12 | $\alpha>1$ |
| 14 | 10 | $\gamma_{\delta}= \D \cap \partial B(\zeta,\delta)$ |
| 24 | 3b | (,) instead of [,] |
| 25 | 10b | proof of Lemma 2.3 |
| 28 | 4 | divide the right side by 2\pi. |
| 29 | 7b | change line to:"follow the proof of Caratheodory's theorem." |
| 35 | 6 | The upper limit in the integral should be $2\pi$ |
| 38 | 2b,4b,7b | solid bar on $\Omega$ |
| 42 | 6 | under a one-to-one and analytic map $\psi$ defined on a neighborhood of $(-1,1)$. |
| 71 | 1 | Worse yet, there exists |
| 74 | 3 | $a \notin \overline{\Omega}$ |
| 76 | 10-11 | the interval [-2,2] should be the complement of the interval [-2,2]. |
| 82 | 7b | the inner integral should have lower limit -L. |
| 83 | 2 | delete second occurence of ``$E_n = \C \setminus \Omega_n$" |
| 89 | 4b | The first integral takes place on the boundary of $\Omega_n$. |
| 95 | 8 | on the behavior |
| 104 | 4 | $\Om \cap E$ should be $\Om\setminus E$ |
| 116 | 5 | 2^k should be 2^n. |
| 116 | 16-18 | commas at end, not periods. |
| 117 | 6,7 | $\Omega_n$ should be $\Omega$ |
| 117 | 6,10,11,13 | s_n should be replaced by r_{n-2} (7 times) |
| 117 | 9 | B_n should be B_{n-2} |
| 117 | 13 | s_n should be replaced by r{n-2} (two places); r_{n} in the numerator should be replaced by r_{n+1} and |z|\le r_n should be |z|\le r_{n+1}. |
| 117 | 17 | s_0 should be r_0 |
| 118 | 4 | s_{2n} should be r_{2n-2} |
| 118 | Figure III.7 | The broken overline on E should be solid. |
| 118 | 4b | The broken overline on E should be solid (three places). |
| 118 | 1b,3b | fraction lines should be solid (6 places). |
| 124 | 6,7 | F^+=F\cap {Im z \ge 0}, F^-=F\cap {Im z <0} |
| 124 | 15 | z should be replaced by w |
| 124 | 2b | z^*=-|Re z|+i Im z |
| 125 | 14 | Extra | before .Then |
| 129 | 1b | III.22 should be III.24 |
| 131 | (1.4),(1.6) | fraction lines should be solid. |
| 133 | 3b | Fuglede, B., Acta Math. 98(1957), 171-219 proved that for any curve family $\Gamma$ we can remove a subset $\Gamma_0$ without affecting the extremal length and find an extremal metric for the family $\Gamma\setminus\Gamma_0$. The removed family $\Gamma_0$ has infinite extremal length (zero modulus). An example is a rectangle with vertical ends E and F. If we add a point z_0 lying on the top edge of the rectangle to E then the extremal distance from E to F is unchanged but the constant metric is no longer extremal since there are short curves from z_0 to F. But if we discard the curves from z_0 to F from the curve family of curves from E to F then the constant metric is extremal, and the length is unchanged. The discarded family is so small that it has infinite extremal length. See Exercise IV.9. |
| 150 | 4b | $\subset \Gamma$ should be $\in \Gamma$ |
| 152 | 17 | Take $z_0\in A$ such that $dist(z_0,B)=dist(A,B)$. |
| 171 | 16-17 | line break too big |
| 172 | 6b-7b | line break too big |
| 195 | 2b | Exercise III.22 should be Exercise III.24(b) |
| 206 | 13b | Lindel\"of's theorem refers to Exercise II.3(d) |
| 206 | 6b | Replace Borel with $\omega$-measurable. |
| 207 | 2 | We should have said there is a subset $A_0$ of $A$ which is an
$F_{\sigma}$, hence Borel, with $\omega(A_0)=1$. Thus $A$ is
$\omega$-measurable. Proof: By Egoroff's theorem and Lemma 3.1, there are closed $K_n$ such that $|\b D\setminus K_n|<1/n$ and such that $\varphi$ is continuous on the compact set $\cup_{K_n}\overline{\Gamma_{\pi/2}(e^{i\theta})}.$ Hence $\varphi(K_n)$ is compact and $\omega(\cup_n \varphi (K_n)) =1.$ Thus A is $\omega$-measurable and (3.2) holds. Continue as in text, except delete the word "also" in the last line of the proof. A proof that A is Borel can be found in S. Mazurkiewicz, "Uber erreichbare Punkte", Fund. Math 26 (1936), 150-155. |
| 209 | Figure VI.3 | The region U is outlined by a thick curve. T_n(w) should have thinner boundary (it is not part of the boundary of U). |
| 210 | Figure VI.4 | There are dashed and dotted lines, which are difficult to discern because the line thicknesses were changed. |
| 212 | 12-14 | Replace the sentence: "The exterior domain ... countable subset of \Gamma." with "If \Gamma' is a copy of \Gamma rotated by 90 degrees and scaled by 1/\sqrt{3} then six copies of \Gamma' in a hexagonal pattern fit exactly along the outer boundary of \Gamma." |
| 212 | 3b | $E \subset \partial \D$ |
| 212 | 11b | "a of measure 0" should be "a set of harmonic measure 0" |
| 220 | 10b | curve, then at |
| 221 | 1,2,4,9,11,13 | $\varphi(G_j)$ should be $\varphi_j(G_j)$ (16 occurances). |
| 221 | table, line 1 | $\varphi_1(G_1)\cap\varphi_2(G_2) \subset T_n(\Gamma)$. |
| 235 | several | overline and fraction bars should be solid (6 places). |
| 239 | 5-11, Fig.VII.5 | for a new version of this see new page 239 |
| 240 | 9b | Kahane's measure from Example 2.6 is *not* a doubling measure, as asserted, because it assigns zero mass to some non-empty open intervals. However, if the construction in Example 2.6 is changed so that the densities satisfy d_{n+1,k} = d_{n,j}/2 when k =4j or 4j+3 and d_{n+1,k} = 3d_{n,j}/2 when k = 4j+1 or 4j + 2 then the limit measure is doubling and singular. |
| 242 | 10b | orientation preserving ACL homeomorphism |
| 252 | 5b,7b | remove 2\pi. |
| 269 | 8-9 | such that if $g(z)$ is a Bloch function on $\D$, then for a.e. $\zeta \in \b\D$ |
| 274 | 5 | (C) should be (c) |
| 276 | 5b & 4b | B(\zeta_1,diam(\gamma)) should be B(w_1,diam(\gamma)) |
| 277 | Figure VIII.1 | No subscript on $D$ or on $\widetilde D$. |
| 282 | 15 | remove black box at end of line |
| 285 | 11 | $\chi_j(\zeta)$ should be $\chi_j(z)$ |
| 285 | 12 | and all $z\in A_1(\zeta)\cap\partial\Om$ |
| 295 | 2b | fraction bars should be solid. |
| 300 | 3b | $\Omega_J$ should be $\Omega_n^J$ |
| 310 | 1 | "bounded universal integral means spectrum" should be boldface. |
| 316 | 8 | liminf not limsup |
| 323 | 12 | change "By the central limit...distribution," to
"By the elementary theory of large deviations (R. Durrett, {\it Probability: Theory and Examples,} 2nd Edition (1996) pp. 70 -76)," |
| 343 | 3&7 | Batakas should be Batakis |
| 367 | 22 | For more details see page 367 correction. |
| 373 | 8b | ||F'|| should be ||F||. |
| 393 | 6b | should be = |
| 393 | 4b-3b | The integrals take place on the unit disk |
| 395 | 7 | (g')^2/2 should be (g')^2 by (1.8) and (6.1). |
| 396 | 2 | (1-|z|^2)^2 |
| 396 | 9b | (1-|z|^2)^3 should be (1-|z|^2) |
| 397-411 | all | for a new version of sections 7 and 8, see new sectX7-X8 |
| 399 | 5b (r.e.) | double dots - should be just one. |
| 400 | 1b (r.e.) | 1 should be 1/2 |
| 435 | 8b | Theorem A.1 (mislabelled) |
| 436 | 9 | Corollary A.2 (mislabelled) |
| 436-439 | various | P_z should not be multiplied by 1/(2\pi) since it is included in the definition. |
| 440 | 14 | "almost everywhere" should be "everywhere". |
| 446 | 6b | See also Tsuji[1959], p. 31 |
| 465 | 5b | contradicts (D.16) |
| 466 | 3 | Corollary D.2 implies |
| 508 | 1 and 2 | should be for a.a. $\theta$ |
| 534 | 15-26 | Betsakos, Betsakos and Solynin references should be before Beurling. |
| 541 | 23 | Iberoamericana |
| 541 | 10b | add page numbers 1-8. |
| 544 | 18 | On V.I. Smirnov domains |
| 549 | 1 | The journal name should be in italics |
| 555-558 | various | add pages: Batakis 343, Durrett 323, Tsuji 446, Lindel\"of 206, Ostrowski 239. |
| 560 | 21b | Tn(\Gamma) page number reference should be 211 (first occurance). |
| 571 | 20-21;col2 | should be a space between Zygmund's theorem and Oksendal conjecture |