重对数律

令${\displaystyle \{Y_{n}\}}$是一列独立同分布的随机变量，其期望为0，方差为1；且记${\displaystyle S_{n}=Y_{1}+\ldots +Y_{n}}$，那么：

${\displaystyle \limsup _{n\to \infty }{\frac {S_{n}}{\sqrt {2n\log \log n}}}=1,\qquad {\text{a.s.}},}$

其中“log”是自然对数，“lim sup”是上极限，“a.s.”是“几乎必然”[3]。

中心极限定理

1. A. Khinchine. "Über einen Satz der Wahrscheinlichkeitsrechnung", Fundamenta Mathematica, 6:9-20, 1924. (The author's name is shown here in an alternate transliteration.)
2. A. Kolmogoroff. "Über das Gesetz des iterierten Logarithmus" （页面存档备份，存于）. Mathematische Annalen, 101:126-135, 1929. (At the Göttinger DigitalisierungsZentrum web site （页面存档备份，存于）)
3. Leo Breiman. Probability. Original edition published by Addison-Wesley, 1968; reprinted by Society for Industrial and Applied Mathematics, 1992. (See Sections 3.9, 12.9, and 12.10; Theorem 3.52 specifically.)