一個有效描述長度、面積、體積和廣義n維體積(內容)如何被可微函數所扭曲的定理。特別是,變量變換定理將弄清內容扭曲的整個問題簡化為理解無窮小的扭曲,即由線性映射的行列式所給出的導數(一個線性映射)的扭曲。
變量變換定理在標准化流中的應用
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