It is shown that the cardinality of the continuum is not real-valued measurable if and only if there exists no nonzero σ-finite diffused measure μ on the real line such that all Vitali sets (respectively all Bernstein sets) are μ-measurable.

中文翻译：

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关于Vitali集和Bernstein集的广义不可测性

结果表明，当且仅当在实线上不存在非零的σ有限扩散度量μ使得所有Vitali集（分别为所有Bernstein集）都是μ度量的，连续体的基数才是不可实测的。