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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

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Universally measurable sets and the perfect set property

Is it true that all universally measurable sets (say on $[0,1]$ ) have the perfect set property? I am not an expert in this at all and the answer may be known, but I was not able to find it. I kno …
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