I am very new to the these topics. I am in a section about Lorentz spaces in Adam's book on Sobolev spaces. What is the intuition in equimeasurable decreasing rearrangement of a function. Given a function $u$ how should I visualize the rearrangement denoted by $u^{*}$? Is it simply about rearranging the values of the function from its highest values to lowest? Any sort of explanation will be helpful.
For example if $u(x)=\frac{\sin(x)}{x}$ how will $u^{*}(x)$ look like?
The relevant section is in chapter 7 of the book Adams, R.A. and Fournier, J.J.F, Sobolev Spaces, 2nd ed., Academic Press, 2003.