A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a mixture of product distributions. Closeness is measured in terms of the relative entropy and an explicit bound is provided. This bound is tighter than those obtained via earlier information-theoretic proofs, and its utility extends to random variables taking values in general spaces. The core argument employed has its origins in the quantum information-theoretic literature.

翻译：利用基本信息论工具，建立了de Finetti表示定理的一种新的有限形式。在一个由$n \geq k$个可交换随机变量构成的向量中，前$k$个随机变量的分布接近于乘积分布的混合。接近程度用相对熵度量，并给出了显式界。该界比通过早期信息论证明得到的界更紧，其适用性可推广至取值于一般空间的随机变量。所采用的核心论证源于量子信息论文献。