The paper considers the classical Bernoulli scheme, that is, a sequence of independent random variables identically distributed with respect to the Lebesgue measure m on the interval [0,1]. The space of realizations of this scheme is the infinite-dimensional cube \({\mathcal{X}} = ({[0,1]^{\mathbb{N}}},\mu )\) with Lebesgue measure μ = m^ℕ. It is proved that there exists a function k(·): (0, 1) → ℝ (which can be defined by k(ε) = C/μ⁵) such that, given any n ∈ ℕ and ε ∈ (0, 1), one can choose a measurable set \({{\mathcal{X}}_{n,\varepsilon }} \subset {\mathcal{X}}\) of measure at least 1 − ε so that the coordinate x_n of any realization \(x = {{\rm{\{ }}{x_n}{\rm{\} }}_n} \in {{\mathcal{X}}_{n,\varepsilon }}\) reaches the first column of the Young P-tableau after at most k(ε)n² insertions of the RSK (Robinson-Schensted-Knuth) algorithm.

本文考虑了经典的伯努利方案，即相对于Lebesgue测度m在[0,1]区间上相同分布的一系列独立随机变量。该方案的实现空间是无穷多维立方体\（{\ mathcal {X}} =（{[0,1] ^ {\ mathbb {N}}}，\ mu）\），Lebesgue测度μ =米^ℕ。证明了存在一个函数ķ（·）：（0,1）→ℝ（其可以定义为ķ（ε）= C /μ ⁵）使得在给定的任何Ñ ∈ℕ和ε∈（0， 1），可以选择一个可测量的集合\（{{\ mathcal {X}} _ {n，\ varepsilon}} \ subset {\ mathcal {X}} \）测量至少1 −ε，以便任何实现的坐标x _n \（x = {{\ rm {\ {}} {x_n} {\ rm {\}}} _ n} \ in {{\ mathcal {X }} _ {n，\ varepsilon}} \）最多插入RSK（Robinson-Schensted-Knuth）算法的k（ε）n ^2次插入后，到达Young P表的第一列。