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where g(x) is some function with mean μ. When the entropy of g(x) is at a maximum and the constraint equations, which consist of the normalization condition <math>\left(1=\int_{-\infty}^\infty g(x)\,dx\right)</math> and the requirement of fixed variance <math>\left(\sigma^2=\int_{-\infty}^\infty g(x)(x-\mu)^2\,dx\right)</math>, are both satisfied, then a small variation δg(x) about g(x) will produce a variation δL about L which is equal to zero:

where g(x) is some function with mean μ. When the entropy of g(x) is at a maximum and the constraint equations, which consist of the normalization condition <math>\left(1=\int_{-\infty}^\infty g(x)\,dx\right)</math> and the requirement of fixed variance <math>\left(\sigma^2=\int_{-\infty}^\infty g(x)(x-\mu)^2\,dx\right)</math>, are both satisfied, then a small variation δg(x) about g(x) will produce a variation δL about L which is equal to zero:

其中 g (x)是平均 μ 的函数。当 g (x)的熵处于最大值时，由归一化条件 < math > 左(1 = int _ {-infty } ^ infty g (x) ，dx 右) </math > 和固定方差 < 左(sigma ^ 2 = int _ {-infty } ^ infty (x)(x)(x-mu) ^ 2，dx 右) </math > 组成的约束方程都满足时，那么关于 g (x)的一个小变化 δg (x)将产生一个等于零的关于 l 的变化 δl:

其中 g (x)是平均 μ 的函数。当 g (x)的熵处于最大值时，由归一化条件 1=∫∞−∞g(x)dx和固定方差σ2=∫∞−∞g(x)(x−μ)2dx组成的约束方程都满足时，那么关于 g (x)的一个小变化 δg (x)将产生一个等于零的关于L的变化δL:

* Differential entropy is in general not invariant under arbitrary invertible maps.

* Differential entropy is in general not invariant under arbitrary invertible maps.