2020S：B0111004Y 实分析
- 第一章 测度论。外测度、可测集、Lebesgue测度、可测函数的基本性质、Littlewood三原则等。 (1-4节)
- 第二章 积分理论。Lebesgue积分的基本性质与收敛定理、可积函数空间$L^1$，Fubini定理及应用。 (1-4节)
- 第三章 微分与积分。积分的微分、Hardy-Littlewood极大函数、Lebesgue微分定理、恒同逼近、函数的可微性。(1-4.0节)
- 第四章 Hilbert空间的初等理论。$L^2$空间、正交性、酉映射、准Hilbert空间、Fourier级数、Fatou定理、闭子空间与正交投影，线性变换及紧算子。 (1-6节)
- 第六章 抽象测度与积分理论。抽象测度空间、测度空间上的积分、乘积测度、广义Fubini定理、Lebesgue-Stieltjes积分、带号测度、测度的绝对连续性。(1-4节)
- 补 充 $L^p$空间。定义、不等式及其空间结构。(使用[2]中第6章1-18节)
- 第七章 Hausdorff测度(1-2节)。
ISBN：978-7-5100-4053-5（世图） or 0-691-11386-6（original version）
- Page 11, Line 4 below (2): rectangles $\to$ cubes
- P12, L6: both R and the complement of R (It may not be accurate, please understand it from the context.)
- P14, L2: choose disjoint cubes
- P14, L-6 ("-" means from bottom): disjoint closed cubes
- P14, L-1: delete the $\infty$ over two $\bigcup$
- P18, L3 in Proof(Pf) of Lem 3.1: a finite cover
- P22, L4: disjoint closed cubes
- P29, in Property 3: $\limsup\limits_{n\to\infty},f_n(x)$ $\to$ $\limsup\limits_{n\to\infty}f_n(x),$
- P53, L8: to be the closure of the set of all (for consistence with the standard definition)
- P53, L10: $supp(f)=\overline{\{x: f(x)\neq 0\}}$ (for consistence with the standard definition)
- P59, L9: positive $\to$ nonnegative
- P61, L-10: $\liminf\limits_{n\to\infty}f_n=\infty$ $\to$ $\liminf\limits_{n\to\infty}\int f_n=\infty$
- P63 L-4 : $2^k\epsilon \leqslant |x|<2^{k+1}\epsilon$
- P63, L-1: $1\leqslant |x|<2$
- P67, in Pf of Thm 1.13, L2: lemma $\to$ proposition
- P78, in step 3, (a), L4: add a "=" before the $\big\{$
- P79, L5: $\chi_{Q_k}$ $\to$ $\chi_{\tilde{Q}_k}$
- P79, L-8: $\mathcal{O}_0$ $\to$ $\tilde{\mathcal{O}}_0$
- P88, L1: Suppose $f\in L^1(\mathbb{R}^d)$ and ...
- P100, L-3: all open balls
- P101, L-7: an open ball
- P103, L-7: open ball
- P106, L-3: $\lim\limits_{m(B)\to 0 \atop \bar{x} \in B}$
- P108, L3 in Cor 1.7: $x$ $\to$ $\bar{x}$
- P109, L-10: $\mathbb{R}^d$ $\to$ $\mathbb{R}^d\setminus \{0\}$
- P110, L10: $|x|<\delta$ $\to$ $|x|\leq \delta$
- P117, L-3: $f$ $\to$ $F$
- P123, L-2: $\{D^+(F)(x)<\infty\}$ $\to $ $\{D^+(F)(x)=\infty\}$
- P124, L10: $G(x)=F(-x)+rx$
- P131, L-9: $f$ $\to$ $F$
- P132, L-1: $\sum\limits_{x\leqslant x_n\leqslant y}$
- P135, L-3: $t_j-1$ $\to $ $t_{j-1}$
- P149, Ex20 Hint, L1: $\chi_K(t)dt$
- P158, L2 below (1): $fg=0$ $\to $ $f\bar{g}=0$
- P168, L2: add "." at the end
- P172, L-7: $k=2|n|+1$ for $n<0$
- P188, L3: an $\to$ and
- P193, L1: $T_nf_n$ $\to$ $Tf_n$
- P193, L8, L17: non-empty $\to$ non-trivial
- P193, L15-L18: $S^\perp$ $\to $ $\mathcal{S}^\perp$
- P227, L2: delete one $\int_0^{2\pi}$
- P272, L11,17,-2: $\mu$ $\to$ $\mu_0$
- P272, L-4: $\mu(F)$ $\to$ $\nu(F)$
- P283, L-15: $(a,b]$ is a Borel ...
- P284, L8: "if" $\to$ "is"
- P315, L-3: $E_j\in\mathcal{M}_j$
- P331, L-1: delete $\beta$
- P332, L10: $z(t)$ $\to $ $\gamma(t)$
- P334, L2: "size" $\to$ "side length"
- P340, L9: $B^{j+1}$
- P340, L10: $\leqslant B|t-s|^\gamma$
- P345, L8: $\leqslant \delta$ (optional)
(Errata updated: Jun. 29, 2020)