Title: An Aldous--Hoover Theorem for Radon Distributions Show Chinese title

Title: 一个关于Radon分布的Aldous--Hoover定理

Abstract: We show that the Aldous--Hoover Theorem, giving representations for exchangeable arrays of Borel-valued random variables, extends to random variables where the common distribution of the random variables is Radon, or even merely compact, a weaker condition that does not even require that the values come from a Hausdorff space. This extends work of Alam \cite{alam2023generalizing} who showed a similar generalization of the di Finetti--Hewitt-Savage Theorem. Show Chinese abstract

Abstract: 我们证明了Aldous–Hoover定理（给出了Borel值随机变量的交换数组的表示）可以扩展到随机变量的情形，其中随机变量的公共分布是Radon分布，甚至是紧致分布，这是一种比Radon分布更弱的条件，甚至不要求取值来自Hausdorff空间。 这推广了Alam的工作，他证明了de Finetti–Hewitt–Savage定理的一个类似推广。 \cite{alam2023generalizing}