一个有效描述长度、面积、体积和广义n维体积(内容)如何被可微函数所扭曲的定理。特别是,变量变换定理将弄清内容扭曲的整个问题简化为理解无穷小的扭曲,即由线性映射的行列式所给出的导数(一个线性映射)的扭曲。
变量变换定理在标准化流中的应用
https://lilianweng.github.io/lil-log/2018/10/13/flow-based-deep-generative-models.html#vae--flows
https://mathworld.wolfram.com/ChangeofVariablesTheorem.html
https://web.williams.edu/Mathematics/sjmiller/public_html/150Sp21/handouts/ChangeVariableThm.pdf
https://web.williams.edu/Mathematics/sjmiller/public_html/probabilitylifesaver/supplementalchap_changeofvar.pdf
http://math.mit.edu/~larsh/teaching/F2007/handouts/changeofvariables.pdf
https://www.whitman.edu/mathematics/calculus_online/section15.07.html
https://archive.lib.msu.edu/crcmath/math/math/c/c210.htm