Symmetric decreasing rearrangement

In mathematics, the symmetric decreasing rearrangement of a function is a function which is symmetric and decreasing, and whose level sets are of the same size as those of the original function. In mathematics, the symmetric decreasing rearrangement of a function is a function which is symmetric and decreasing, and whose level sets are of the same size as those of the original function. Given a measurable set, A {displaystyle A} , in Rn , one defines the symmetric rearrangement of A {displaystyle A} , called A ∗ {displaystyle A^{*}} , as the ball centered at the origin, whose volume (Lebesgue measure) is the same as that of the set A {displaystyle A} .