Universally measurable set

In mathematics, a subset ${\displaystyle A}$ of a Polish space ${\displaystyle X}$ is universally measurable if it is measurable with respect to every complete probability measure on ${\displaystyle X}$ that measures all Borel subsets of ${\displaystyle X}$. In particular, a universally measurable set of reals is necessarily Lebesgue measurable (see #Finiteness condition below).

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