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        "quote": "两个几乎处处相等的局部可积函数 $f$ 与 $g$ 给出相同的分布 $T _ { f } = T _ { g }$。反之，若对所有试验函数 $\\varphi$ 都有 $T _ { f } ( \\varphi ) = T _ { g } ( \\varphi )$，则密度函数 $f$ 与 $g$ 几乎处处相等。一个概要证明如下：设 $I ^ { n }$ 为闭区间 $I ^ { n } = I _ { 1 } \\times I _ { 2 } \\times \\cdot \\cdot \\cdot \\times I _ { n }$ 的任意乘积，并选取一个试验函数 $\\varphi$ 任意接近单位阶梯函数 $\\chi _ { I ^ { n } }$。于是 $\\textstyle \\int _ { I ^ { n } } ( f - g ) \\mathrm { d } \\mu ^ { n } = 0$，而这对所有 $I ^ { n } \\operatorname { i f } f - g$ 都不可能，如果其非零正部分 $( f - g ) ^ { + } > 0$ 在一个正测度集合上成立。这一论证可以很容易地加以改进，以证明 $f - g = 0$ 几乎处处成立。因此，密度 $f$ 由 $T _ { f }$ 唯一确定，至多在一个测度为零的集合上除外。通过将 $f$ 与 $T _ { f } { \\mathrm { : } }$ 等同起来，局部可积函数可以被视为分布。然而，并非所有分布都以这种方式产生；具有密度 $T = T _ { f }$ 的分布有时被称为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:ef60bda0-3f62-4112-9dfa-81af9938599d\" data-concept-route=\"/concept-identities#concept-ef60bda0-3f62-4112-9dfa-81af9938599d\" id=\"first-e85f7b05eafc32f7475c-zh\">正则分布(regular distribution)</u>，而那些不对应于任何局部可积函数的分布则称为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:704f26e9-640a-4a8e-bdd2-2b6d97745986\" data-concept-route=\"/concept-identities#concept-704f26e9-640a-4a8e-bdd2-2b6d97745986\" id=\"first-dad6ecca9ad2131a8c8e-zh\">奇异分布(singular distribution)</u>。",
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