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==Definition==
==Definition定义==
Let <math>X</math> be a random variable with a [[probability density function]] <math>f</math> whose [[support (mathematics)|support]] is a set <math>\mathcal X</math>. The ''differential entropy'' <math>h(X)</math> or <math>h(f)</math> is defined as<ref name="cover_thomas">{{cite book|first1=Thomas M.|first2=Joy A.|last1=Cover|last2=Thomas|isbn=0-471-06259-6|title=Elements of Information Theory|year=1991|publisher=Wiley|location=New York|url=https://archive.org/details/elementsofinform0000cove|url-access=registration}}</ref>
Let <math>X</math> be a random variable with a [[probability density function]] <math>f</math> whose [[support (mathematics)|support]] is a set <math>\mathcal X</math>. The ''differential entropy'' <math>h(X)</math> or <math>h(f)</math> is defined as<ref name="cover_thomas">{{cite book|first1=Thomas M.|first2=Joy A.|last1=Cover|last2=Thomas|isbn=0-471-06259-6|title=Elements of Information Theory|year=1991|publisher=Wiley|location=New York|url=https://archive.org/details/elementsofinform0000cove|url-access=registration}}</ref>
<math>h(X+c) = h(X)</math>
<math>h(X+c) = h(X)</math>