# Ask for help on understanding a formula related to change of variable

Although I have tried for a long time, I cannot understand Eq.(11) of paper "Microfacet Models for Refraction through Rough Surfaces" written by Bruce Walter, Stephen Marschner, Hongsong Li and Kenneth Torrance, Eurographics Symposium on Rendering(2007). My knowledge of change of variable is no more than what are described in this webpage: http://tutorial.math.lamar.edu/Classes/CalcIII/ChangeOfVariables.aspx. Because I am not a smart people, can you please help me understand how this equation is derived based on the knowledge of that webpage and in a way that a common human can follow? Specifically, one of the questions I cannot answer is: what is the variable to be changed and changed to, $$\mathbf{i}$$, $$\mathbf{o}$$ or $$\mathbf{m}$$? The paper is famous so it can be easily found from Google search. For your convenience, I copied the pertaining page here. Thank you for your help.