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Stein & Shakarchi: Real Analysis 2013重印版勘误表(非官方，仅供参考)

1. Page 11, Line 4 below (2): rectangles $\to$ (表示替换为, 下同) cubes
2. P12, L6: both R and the complement of R (It may not be accurate, please understand it from the context.)
3. P14, L2: choose disjoint cubes
4. P14, L-6 (``-'' means from bottom): disjoint closed cubes
5. P14, L-1: delete the $\infty$ over two $\bigcup$
6. P18, L3 in Proof (Pf) of Lem 3.1: a finite cover
7. P22, L4: disjoint closed cubes
8. P29, in Property 3: $\limsup\limits_{n\to\infty},f_n(x)$ $\to$ $\limsup\limits_{n\to\infty}f_n(x),$
9. P53, L8: to be the closure of the set of all (for consistence with the standard definition)
10. P53, L10: $\mathrm{supp}(f)=\overline{\{x: f(x)\neq 0\}}$ (for consistence with the standard definition)
11. P56, L8-9: delete ``a.e.''
12. P59, L9: positive $\to$ non-negative
13. P61, L-10: $\liminf\limits_{n\to\infty}f_n=\infty$ $\to$ $\liminf\limits_{n\to\infty}\int f_n=\infty$
14. P63 L-4 : $2^k\epsilon \leqslant |x|<2^{k+1}\epsilon$
15. P63, L-1: $1\leqslant |x|<2$
16. P67, in Pf of Thm 1.13, L2: lemma $\to$ proposition
17. P78, in step 3, (a), L4: add a ``='' before the $\big\{$
18. P79, L5: $\chi_{Q_k}$ $\to$ $\chi_{\tilde{Q}_k}$
19. P79, L-8: $\mathcal{O}_0$ $\to$ $\tilde{\mathcal{O}}_0$
20. P88, L1: Suppose $f\in L^1(\mathbb{R}^d)$ and ...
21. P100, L-3: all open balls
22. P101, L-7: an open ball
23. P103, L-7: open ball
24. P106, L-3: $\lim\limits_{m(B)\to 0 \atop \bar{x} \in B}$
25. P108, L3 in Cor 1.7: $x$ $\to$ $\bar{x}$
26. P109, L-10: $\mathbb{R}^d$ $\to$ $\mathbb{R}^d\setminus \{0\}$
27. P110, L10: $|x|<\delta$ $\to$ $|x|\leq \delta$
28. P117, L-3: $f$ $\to$ $F$
29. P123, L-2: $\{D^+(F)(x)<\infty\}$ $\to $ $\{D^+(F)(x)=\infty\}$
30. P124, L10: $G(x)=F(-x)+rx$
31. P131, L-9: $f$ $\to$ $F$
32. P132, L-1: $\sum\limits_{x\leqslant x_n\leqslant y}$
33. P135, L-3: $t_j-1$ $\to $ $t_{j-1}$
34. P149, Ex20 Hint, L1: $\chi_K(t)dt$
35. P158, L2 below (1): $fg=0$ $\to $ $f\bar{g}=0$
36. P168, L2: add ``.'' at the end
37. P172, L-7: $k=2|n|+1$ for $n<0$
38. P188, L3: an $\to$ and
39. P193, L1: $T_nf_n$ $\to$ $Tf_n$
40. P193, L8, L17: non-empty $\to$ non-trivial
41. P193, L15-L18: $S^\perp$ $\to $ $\mathcal{S}^\perp$
42. P204, Pb.8, L3: $a_{k-j}$ $\to$ $a_{k-j}^2$
43. P227, L2: delete one $\int_0^{2\pi}$
44. P272, L11,17,-2: $\mu$ $\to$ $\mu_0$
45. P272, L-4: $\mu(F)$ $\to$ $\nu(F)$
46. P282, in Theorem 3.5, L5: $F(x)=-\mu((x,0])$, $x<0$
47. P283, L-15: $(a,b]$ is a Borel ...
48. P284, L8: ``if '' $\to$ ``is''
49. P289, L-9: $\limsup_{n\to \infty} E_n$ $\to$ $\limsup_{n\to \infty} E_n^*$
50. P291, L-2: $\nu_{j,a}=f_jd\mu_j$ $\to$ $d\nu_{j,a}=f_jd\mu_j$
51. P312, Ex.1, L1: ``a non-empty collection'' $\to$ ``an algebra''; L2: delete ``complements and''
52. P315, L-3: $E_j\in\mathcal{M}_j$
53. P331, L-1: delete $\beta$
54. P332, L10: $z(t)$ $\to $ $\gamma(t)$
55. P334, L2: ``size'' $\to$ ``side length''
56. P340, L9: $B^{j+1}$
57. P340, L10: $\leqslant B|t-s|^\gamma$
58. P345, L8: $\leqslant \delta$ (optional)