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→Nonnegativity 非负性
:<math>I(X;Y|Z) \ge 0</math>,
:<math>I(X;Y|Z) \ge 0</math>,
for discrete, jointly distributed random variables <math>X</math>, <math>Y</math> and <math>Z</math>. This result has been used as a basic building block for proving other [[inequalities in information theory]], in particular, those known as Shannon-type inequalities. Conditional mutual information is also non-negative for continuous random variables under certain regularity conditions.<ref>{{cite book |last1=Polyanskiy |first1=Yury |last2=Wu |first2=Yihong |title=Lecture notes on information theory |date=2017 |page=30 |url=http://people.lids.mit.edu/yp/homepage/data/itlectures_v5.pdf}}</ref>
for discrete, jointly distributed random variables <math>X</math>, <math>Y</math> and <math>Z</math>. This result has been used as a basic building block for proving other [[inequalities in information theory]], in particular, those known as Shannon-type inequalities. Conditional mutual information is also non-negative for continuous random variables under certain regularity conditions.<ref>{{cite book |last1=Polyanskiy |first1=Yury |last2=Wu |first2=Yihong |title=Lecture notes on information theory |date=2017 |page=30 |url=http://people.lids.mit.edu/yp/homepage/data/itlectures_v5.pdf}}</ref>
对于离散，联合分布的随机变量X，Y和Z，如下不等式永远成立：
对于离散，联合分布的随机变量X，Y和Z，如下不等式永远成立：
该结果已被用作证明信息理论中其他不等式的基础，尤其是香农不等式。对于某些正则条件下的连续随机变量，条件交互信息也是非负的。
该结果已被用作证明信息理论中其他不等式的基础，尤其是香农不等式。对于某些正则条件下的连续随机变量，条件交互信息也是非负的。
=== Interaction information 交互信息 ===
=== Interaction information 交互信息 ===