Last Updated:2025/11/26

On a locally compact Hausdorff space, the Borel measure is inner regular, so the measure of any Borel set equals the supremum of the measures of compact subsets contained in it.

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On a locally compact Hausdorff space, the Borel measure is inner regular, so the measure of any Borel set equals the supremum of the measures of compact subsets contained in it.

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局所コンパクトなハウスドルフ空間上で、ボレル測度は内正則(内部からコンパクト集合で近似できる)であるため、任意のボレル集合の測度はそれに含まれるコンパクト部分集合の測度の上限に等しい。

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