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        "quote": "> [!exercise] <a class=\"object-permalink\" href=\"#problem-11-11\">习题 11.11</a> \n>\n> 集合$E$的<u class=\"concept-term\" data-concept-identity=\"urn:uuid:496d1b66-73ef-4e6a-965e-6e67183f7c50\" data-concept-route=\"/concept-identities#concept-496d1b66-73ef-4e6a-965e-6e67183f7c50\" id=\"first-cda9152c54ea73af72d4-zh\">内测度(inner measure)</u> $\\mu _ { * } ( E )$定义为$E$的所有可测子集的测度的最小上界。证明$\\mu _ { * } ( E ) \\leq \\mu ^ { * } ( E )$\n>\n> 对任意开集 $U \\supset E$，证明\n>\n> $$\n> \\mu (U) = \\mu_ {*} (U \\cap E) + \\mu^ {*} (U - E)\n> $$\n>\n> 并且 $E$ 可测且具有有限测度，当且仅当 $\\mu _ { * } ( E ) = \\mu ^ { * } ( E ) < \\infty$",
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