Consider we have a measurable subset $A$ of euclidean space $\mathbb{R}^p$ with respect to Lebesgue measure. Is it always measurable in respect to any measure function (I mean non-negative,finite,regular and additive measures here) or there is situation which it may or may not measurable depending on measure function? Under which measure function conditions, an specified set is always measurable?
2026-04-29 09:45:23.1777455923
Is it possible that a set be measurable with a measure function but not with the other?
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