Interpolation of Level Sets for Equimeasurable Functions

The author proves a new theoretical property for the family of rearrangements R f. of a given measurable function f. Given a finite number of equimeasurable functions f1, . . . , fngR f., it is possible to construct a family of equimeasurable functions h . ;R f.which interpolates the functions f , . . . , f in a convex- l lgw0, 1x 1 n like way. However, as an application, this interpolation result yields a compact fixed point property