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        "quote": "> [!example] <a class=\"object-permalink\" href=\"#example-11-4\">例 11.4</a> \n>\n> 定义在集合 $X$ 上的西格玛代数上，一个偶尔有用的测度是 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:adc2298d-a628-495d-aacf-599f09c84dd9\" data-concept-route=\"/concept-identities#concept-adc2298d-a628-495d-aacf-599f09c84dd9\" id=\"first-b0f5a78d1efe2358093f-zh\">狄拉克测度(Dirac measure)</u>。设 $a$ 为 $X ,$ 的任意固定点，并令\n>\n> $$\n> \\delta_ {a} (A) = \\left\\{ \\begin{array}{l l} 1 & \\text { if } a \\in A, \\\\ 0 & \\text { if } a \\notin A. \\end{array} \\right.\n> $$\n>\n> (Meas4) 对 $\\mu = \\delta _ { a }$ 显然成立，而 (Meas5) 则可由以下明显事实推出：一个不相交集合族 $\\left\\{ A _ { i } \\right\\}$ 的并集能包含 $a$，当且仅当 $a\\in A _ { j }$ 恰好对一个成员 $A _ { j }$ 成立。该测度在分布理论中有应用，见第 12 章。",
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