Independently scattered random measures are usually defined and constructed under the additional condition of being infinitely divisible, a rather strong condition. A more natural condition is the assumption that the random measure has no atoms, that is being atomless. We show that atomless random measures on δ-rings are necessarily infinitely divisible, so infinite divisibility is in fact a quite natural condition.

中文翻译：

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关于 δ 环的无原子随机测度

独立分散的随机测度通常是在无限可分的附加条件下定义和构造的，这是一个相当强的条件。更自然的条件是假设随机度量没有原子，即无原子。我们证明 δ 环上的无原子随机测度必然是无限可分的，因此无限可分实际上是一个非常自然的条件。