Abstract:The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on R n . Rearrangements are maps that are monotonic (up to sets of measure zero) and equimeasurable, i.e., they preserve the measure of super-level sets of functions. All the principal known symmetrization processes for functions, such as Steiner and Schwarz symmetrization, are rearrangements, and these have a multitude of applications in diverse areas of the mathematical s… Show more
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