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Disintegration theorem
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<p> In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the disintegration theorem is a result in <a href="/facts/Measure_theory/yCq7zlI4">measure theory</a> and <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>. It rigorously defines the idea of a non-trivial "restriction" of a <a href="/facts/Measure_(mathematics)/yCq7zlI4">measure</a> to a <a href="/facts/Measure_zero/kMudL8Mn">measure zero</a> subset of the <a href="/facts/Measure_space/w9Dx4KY1">measure space</a> in question. It is related to the existence of <a href="/facts/Conditioning_(probability)/K68RrXFD">conditional probability measures</a>. In a sense, "disintegration" is the opposite process to the construction of a <a href="/facts/Product_measure/KyL0bbNy">product measure</a>. </p>