For qualitative probability spaces, monotone continuity and third-order atom-swarming are together sufficient for a unique countably additive probability measure representation that may have atoms (Mackenzie in Theor Econ 14:709–778, 2019). We provide a new proof by appealing to a theorem of Luce (Ann Math Stat 38:780–786, 1967), highlighting the usefulness of extensive measurement theory (Krantz et al. in Foundations of Measurement Volume I: Additive and Polynomial Representations. Academic Press, New York, 1971) for economists.

中文翻译：

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关于原子群和卢斯概率信念定理

对于定性概率空间，单调连续性和三阶原子群组合足以满足可能具有原子的唯一可数加性概率度量表示形式（Mackenzie in Theor Econ 14：709-778，2019）。我们通过引用卢斯定理（Ann Math Stat 38：780–786，1967），强调广泛的测量理论的有效性（Krantz等人在《基础测量卷I：加法和多项式表示》中提供了新证据）。出版社，纽约，1971年）。